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## Mathematics Questions

Question 1
A web publisher provides information on travelling to China. Access to the website is free but revenues are generated by selling ads that are posted on the website. In the following month, the website has committed to display ads to 650,000 viewers, i.e., 650,000 impressions. Based on data from previous months the traffic to the website is estimated to be normally distributed with a mean of 850,000 viewers and a standard deviation of 150,000. (You need to use a normal table or Excel for this question.)
a) What is the probability that the web publisher will be able to deliver the promised impressions?
b) How many impressions should the web publisher have taken on, to be able to guarantee a 95% service level?
Question 2
Which one of the following statements is true?
a) If we know the mean of the normal distribution we know its shape
b) In the normal distribution, the mean, median, mode, and standard deviation are all at the same position on the horizontal axis since the distribution is symmetric.
c) Normal distribution that is wide has a high standard deviation
Question 3
ABC Fund Managers Plc claims that the monthly returns to their high-income tracker fund exceed the index return by 0.003 (i.e. 0.3%). Over a one-year period the average amount by which the tracker fund exceeds the index is 0.001. The standard deviation of the difference is calculated as 0.004 over this period. Explain how you can test the claim using a one-tailed hypothesis test.

# MATH 221 Week 8 Final Exam

MATH 221 Final Exam

1. (TCO 9) The annual Salary of an electrical engineer is given in terms of the years of experience by the table below. Find the equation of linear regression for the above data and obtain the expected salary for an engineer with 45 years of experience. Round to the nearest \$100.
2. (TCO 5) A company produces window frames. Based on a statistical analysis, we found that 15% of their product is defective. They have shipped 10 windows to one of their customers. The customer is worried about the probability of having defective frames. Choose the best answer of the following:
3. (TCO 5) A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering 3 OR 4 questions correctly.
4. (TCO 5) It has been recorded that the average number of errors in a newspaper is 4 mistakes per page. What is the probability of having 1 or 2 errors per page?
5. (TCO 2) The median height of the players on a high school basketball team is 68 inches. What does this tell you about the typical height of a player on this team?
6. (TCO 6) Using the standard normal distribution, find the probability that z is greater than 1.78
7. (TCO 8) The mean age of school bus drivers in Denver is claimed to be 56.9 years. A hypothesis test is performed at a level of significance of 0.01 with a P-value of 0.09. Choose the best interpretation of the hypothesis test.

8.(TCO 8) A poll of U.S. health professionals revealed less than 82% would choose the same career. In a hypothesis test conducted at a level of significance of 1%, a P-value of 0.035 was obtained. Choose the best interpretation of the hypothesis test.
9.(TCO 2) You are going to take a statistics class next session. You have two professors to choose from. Both professors have a mean performance evaluation score of 3.56 out of 4. Professor A has a standard deviation of .86 while Professor B has a standard deviation of .51. You want to choose the better professor because math is a challenge for you, who do you choose?
10.(TCO 4) A travel agency offers 4 different vacation packages to Europe. Their net profit for package 1 is \$500, for package 2 it is \$750, for package 3 it is \$900, and for package 4 it is \$1,500. From past experience they know that 20% of their customers purchase package 1, 15% of their customers purchase package 2, 40% of their customers purchase package 3 and 25% of their customers purchase package 4. Find the expected value or average profit per customer and determine how much profit they should expect if 10 people purchase one of their European vacation packages.
11.(TCO 3) The ages of 25 employees in a company are listed below: Use the stem & leaf plot to determine the shape of the distribution. Choose the best answer.
12.(TCO 1) A statistician is considering using a 99% confidence interval for a study instead of a 95% confidence interval. What happens to the required sample size if the confidence level is increased from 95% to 99% and the same error is required in each case?
13.(TCO 6) Scores on an assessment exam at a private school are normally distributed, with a mean of 75 and a standard deviation of 11. Any student who scores in the top 7% is eligible for a scholarship. What is the lowest whole number score you can earn and still be eligible for a scholarship?
14.(TCO 5) A shipment of 40 computers contains five that are defective. How many ways can a small business buy three of these computers and receive no defective ones?

1. (TCO 6) The time required to make 1100 gallons of synthetic rubber at a plant in South America in a recent year was normally distributed with a mean of 16 hours and a standard deviation of 3 hours. What is the probability that it will take more than 19 hours to make 1100 gallons of synthetic rubber?

16.(TCO 10) The annual rice yield (in pounds), is given by the equation y-hat = 859 + 5.76a + 3.82b, where ‘a’ is the number of acres planted (in thousands), and ‘b’ is the number of acres harvested (in thousands). Predict the annual rice yield (in pounds) when the number of acres planted is 2550 (in thousands) and the number of acres harvested is 2245 (in thousands).

1. (TCO 9) Describe the correlation in this graph.

Page 2
1.(TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.
2.(TCO 11) A 15-minute Oil and Lube service claims that their average service time is no more than 15 minutes. A random sample of 35 service times was collected, and the sample mean was found to be 16.2 minutes, with a sample standard deviation of 3.5 minutes. Is there evidence to support, or to reject the claim at the alpha = 0.05 level? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. Writing the formal conclusion is an important part of the process.
3.(TCO 5) The probability that a house in an urban area will be burglarized is 5%. If 50 houses are randomly selected, what is the probability that one of the houses will be burglarized? (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability that, out of 50 houses, exactly 4 of the houses will be burglarized. Show your calculations or explain how you found the probability.
4.(TCO 6) The average monthly gasoline purchase for a family with 2 cars is 90 gallons. This statistic has a normal distribution with a standard deviation of 10 gallons. A family is chosen at random.
5.(TCO 8) An engineering firm is evaluating their back charges. They originally believed their average back charge was \$1800. They are concerned that the true average is higher, which could hurt their quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample mean back charge to be \$1950. If the standard deviation of back charges is \$500, and alpha = 0.04, should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.
6.(TCO 7) A marketing firm wants to estimate the average amount spent by patients at the hospital pharmacy. For a sample of 200 randomly selected patients, the mean amount spent was \$92.75 and the standard deviation \$13.10. (a) Find a 95% confidence interval for the mean amount spent by patients at the pharmacy. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.
7.(TCO 7) A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 15 people with the condition currently untreated. From this small sample, the mean heart rate is 92 beats per minute with a standard deviation of 8. (a) Find a 98% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.
8.(TCO 2) The heights of 10 sixth graders are listed in inches: {50, 62, 54, 57, 60, 57, 53, 57, 59, 58}. (a) Find the mean, median, mode, sample variance, and range. (b) Do you think that this sample might have come from a normal population? Why or why not?

# The Pythagorean Theorem

Assignment 1: The Pythagorean Theorem

Geometry is a very broad field of mathematics composed of a wide range of tools that can be used for problem solving. In this module, you are going to research three examples of the implementation of geometry that would employ the use of the Pythagorean Theorem as a problem-solving tool.
The examples you find can come from several different fields of study and applications such as construction, city planning, highway maintenance, art, architecture, and communications, to name a few. The examples you find must clearly demonstrate the use of the Pythagorean Theorem as a tool. Your textbook—Chapter 10, “Modeling with Geometry”—would be a good reference to consult for some examples illustrating the use of the Pythagorean Theorem in applied situations.
For each example you share in your post, address the following:

• Demonstrate the use of the Pythagorean Theorem in the solution of this problem.
• How is the Pythagorean Theorem applied to help solve this problem in this application?
• Why would the Pythagorean Theorem be applied instead of employing some other mathematical tool?
• What tools, unique to this application, would be necessary to get the measurements needed to apply the Pythagorean Theorem?
• Are there other geometrical concepts that are necessary to know in order to solve this problem?
• Are there any modern tools that help solve this kind of problem that either provide a work around, or that rely heavily upon, the Pythagorean Theorem?

When constructing your response, consider the theories, examples, and concepts discussed in your readings this module, and refer to them to support your conclusions.
Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.
By Saturday, July 11, 2015, post your response to the appropriate Discussion Area. Through Wednesday, July 15, 2015, review the postings of your peers and respond to at least two of them. Consider commenting on the following:

• What other geometrical tools do you feel are necessary to understand in order to solve the examples provided besides the Pythagorean Theorem?
• Do you think we would have the technology that we have today without knowledge of mathematical problem-solving tools such as the Pythagorean Theorem? Explain.

Assignment 1: The Pythagorean Theorem

Geometry is a very broad field of mathematics composed of a wide range of tools that can be used for problem solving. In this module, you are going to research three examples of the implementation of geometry that would employ the use of the Pythagorean Theorem as a problem-solving tool.
The examples you find can come from several different fields of study and applications such as construction, city planning, highway maintenance, art, architecture, and communications, to name a few. The examples you find must clearly demonstrate the use of the Pythagorean Theorem as a tool. Your textbook—Chapter 10, “Modeling with Geometry”—would be a good reference to consult for some examples illustrating the use of the Pythagorean Theorem in applied situations.
For each example you share in your post, address the following:

• Demonstrate the use of the Pythagorean Theorem in the solution of this problem.
• How is the Pythagorean Theorem applied to help solve this problem in this application?
• Why would the Pythagorean Theorem be applied instead of employing some other mathematical tool?
• What tools, unique to this application, would be necessary to get the measurements needed to apply the Pythagorean Theorem?
• Are there other geometrical concepts that are necessary to know in order to solve this problem?
• Are there any modern tools that help solve this kind of problem that either provide a work around, or that rely heavily upon, the Pythagorean Theorem?

When constructing your response, consider the theories, examples, and concepts discussed in your readings this module, and refer to them to support your conclusions.
Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.
By Saturday, July 11, 2015, post your response to the appropriate Discussion Area. Through Wednesday, July 15, 2015, review the postings of your peers and respond to at least two of them. Consider commenting on the following:

• What other geometrical tools do you feel are necessary to understand in order to solve the examples provided besides the Pythagorean Theorem?
• Do you think we would have the technology that we have today without knowledge of mathematical problem-solving tools such as the Pythagorean Theorem? Explain.

Assignment 1: The Pythagorean Theorem

Geometry is a very broad field of mathematics composed of a wide range of tools that can be used for problem solving. In this module, you are going to research three examples of the implementation of geometry that would employ the use of the Pythagorean Theorem as a problem-solving tool.
The examples you find can come from several different fields of study and applications such as construction, city planning, highway maintenance, art, architecture, and communications, to name a few. The examples you find must clearly demonstrate the use of the Pythagorean Theorem as a tool. Your textbook—Chapter 10, “Modeling with Geometry”—would be a good reference to consult for some examples illustrating the use of the Pythagorean Theorem in applied situations.
For each example you share in your post, address the following:

• Demonstrate the use of the Pythagorean Theorem in the solution of this problem.
• How is the Pythagorean Theorem applied to help solve this problem in this application?
• Why would the Pythagorean Theorem be applied instead of employing some other mathematical tool?
• What tools, unique to this application, would be necessary to get the measurements needed to apply the Pythagorean Theorem?
• Are there other geometrical concepts that are necessary to know in order to solve this problem?
• Are there any modern tools that help solve this kind of problem that either provide a work around, or that rely heavily upon, the Pythagorean Theorem?

When constructing your response, consider the theories, examples, and concepts discussed in your readings this module, and refer to them to support your conclusions.
Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.
By Saturday, July 11, 2015, post your response to the appropriate Discussion Area. Through Wednesday, July 15, 2015, review the postings of your peers and respond to at least two of them. Consider commenting on the following:

• What other geometrical tools do you feel are necessary to understand in order to solve the examples provided besides the Pythagorean Theorem?
• Do you think we would have the technology that we have today without knowledge of mathematical problem-solving tools such as the Pythagorean Theorem? Explain.

# z Scores, Type I and II Error, Null Hypothesis Testing

This is your second IBM SPSS Assignment.

It includes three sections. You will:

Generate z scores for a variable in grades.sav and report/interpret them.
Analyze cases of Type I and Type II error.
Analyze cases to either reject or not reject a null hypothesis.
The format of this assignment should be narrative with supporting statistical output (table and graphs) integrated (see the Copy/Export Output Instructions in the Resources area for how to do this) into the narrative in the appropriate place (not all at the end of the document).

Download the Unit 4 Assignment 1 Answer Template from the Resources area and use the template to complete the following sections:

Section 1: z Scores in SPSS.
Section 2: Case Studies of Type I and Type II Error.
Section 3: Case Studies of Null Hypothesis Testing.
Submit your assignment as an attached Word document in the assignment area. All weekly assignments are due by the end of the week on Sunday at 11:59 pm CST.

Studies
Use your Warner text to complete the following:

Read Chapter 3, “Statistical Significance Testing,” pages 81–124. This reading addresses the following topics:
The Logic of Null Hypothesis Testing (NHST).
Type I and Type II Error.
The z Test.
Null Hypothesis and Alternative Hypothesis.
Limiting Type I Error.
Effect Size.
Statistical Power.

To successfully complete this learning unit, you will be expected to:

Calculate z scores in SPSS and interpret them.
Analyze case studies of Type I and Type II error.
Analyze case studies of null hypothesis testing.

## Null and alternative hypothesis

1. A stationary store owner knows the mean retail value of greeting cards last year was \$2.50. She believes that the mean value of the cards this year has increased. Develop the null and alternative hypothesis most appropriate for this situation. (1 pt)
HO: μ “Click here to state the null hypothesis.”
HA: μ “Click here to state the alternativel hypothesis.”
2. Consider the following hypothesis test:
H_0: μ=25
H_A: μ≠25
A sample of 57 items provided a sample mean of 28.1. The population standard deviation is 8.46. use the critical value approach, at α = 0.05. Answer the following three questions. (1 pt, 1 pt, 1 pt)
a. “Click here and state the rejection rule”
b. “Click here to show the computed test statistic.”
c. “Click here to state if you reject or fail to reject the null hypothesis.”
3. Consider the following hypothesis test:
H_0: μ≤1200
H_A: μ>1200
A sample of 113 items provided a sample mean of 1215. The population standard deviation is 100. Use the p-value approach, at α = 0.05. Answer the following three questions. (1 pt, 1 pt, 1 pt)
a. “Click here and state the rejection rule”
b. “Click here to show the computed test statistic.”
c. “Click here to state if you reject or fail to reject the null hypothesis.”
4. A hole-punch machine is set to punch a hole 1.84 centimeters in diameter in a strip of sheet metal in a manufacturing process. It is important to future steps in the process that the hole be punched to the specified diameter of 1.84 centimeters. A sample of 12 strips of sheet metal produced a mean diameter of 1.85 centimeters and a sample standard deviation of 0.024 centimeters At α = 0.05 does this sample show evidence that the true mean diameter differs from 1.84 centimeters? Justify your answer using the t-distribution and the critical value approach. (2 pts)

# Units of Measurement

The kitchen may be the one room in which most people are most aware of the different systems and units of measurements used in the house and around the world. In the United States (U.S.), milk is bought by the gallon, sugar by the pound, soda by the liter, and cereal by the ounce. After you unpack your groceries you store some in the freezer at 0°F or indulge in a snack by baking a treat in your preheated oven at 350°F. As you can see, you can encounter many different units of measure just in the kitchen.

The units used to measure today have been used throughout history, but does everyone use the same standard system of measurement? Currently the U.S., Liberia, and Burma are the only countries that do not use the System Internationale (SI), or more commonly known as the metric system. The units of measurement in the U.S. are based on the English Imperial system.

To start this week’s Discussion pick out a simple recipe that is given in the English Imperial system (select one from the internet if you do not have one of your own) and address the following questions:

1. Convert the ingredients in your recipe from its original imperial units into metric units. Post both the original and converted recipe in the same post so that your classmates and instructor can look at the differences. There is no need to post the preparation or cooking instructions—only the ingredients.
2. Was it difficult to make the conversion from one system of units to the other? Why, or why not?
3. Time to shift your focus to another system of measurements. Now, use an online mapping program to find out how far you will have to travel to get to one of Kaplan’s graduation ceremonies (in Chicago, IL or Miami, FL) from your hometown. Approximately how far in miles and in kilometers will you have to travel?
4. What if you wanted to know what the distance would be in smaller units? In the imperial system you could convert miles into yards and feet. Using SI units you could convert kilometers into meters and centimeters.
1. Convert the data from question 3 into the number of feet and meters you will have to travel.
2. Which system (Imperial or SI) did you find easier to calculate the smaller distances in? Why?
5. Humans have used different systems of measurement throughout history. Do some research on your own, and find a unit of measurement that you did not know about before and give a brief description of its history. Explain how to convert it into a unit of measurement that people would be familiar with today.

## Linear Programming

Assignment

1. The garden center at a local home improvement store must allocate its space. In particular, it must decide how many square feet to devote to each of two types of products: plants (P≥0, measured in square feet) and supplies (S≥0, measured in square feet). The garden center earns \$0.10 profit (per day) for each square foot of space devoted to plants and \$0.05 (per day) for each square foot of space devoted to supplies. The garden center faces the following constraints:
• The garden center can devote no more than 10 thousand square feet to these products (combined).
• Based upon past experience, the amount of space devoted to supplies should be at least three times as large as that devoted to plants.

Type the following sentences, deleting the blanks and replacing them with numbers (rounding all numbers to the nearest integer).

“In order to maximize profit, the garden center should devote _____ square feet to plants and ______ square feet to supplies. If it makes this choice, its daily profit will be \$______.”

1. The manager of a local television station is trying to decide the best daily mix of the two types of programs that the station airs – network shows (N≥0, measured in hours) and local shows (L≥0, measured in hours). He is trying to maximize the station’s advertising revenue. Each hour of network programming (on average) earns \$60,000 of advertising revenue. Each hour of local programming earns (on average) \$16,000 of advertising revenue. The station faces the following constraints:
• The station can’t broadcast more than 24 hours of programming each day.
• Network programming costs (on average) \$50,000 per hour, while local programming costs (on average) \$10,000 per hour. The station’s budget allows for spending up to \$500,000 per day on programming.

Type the following sentences, deleting the blanks and replacing them with numbers (rounding all numbers to one decimal):

“In order to maximize advertising revenue, the station should devote _____ hours to network programming and ______ hours to local programming. If it makes this choice, its advertising revenue will be \$______.”

1. Wal-Mart, Target and other retailers are implementing schedule-optimization systems to cut their labor costs. Suppose that Wal-Mart hires two types of workers, full-time and part-time. Let F be the number of full-time hours used in a typical day. Let P be the number of part-time hours used. (Assume that fractional hours can be used.) Part-time workers cost \$10 per hour and full-time workers cost \$18 an hour. Wal-Mart’s goal is to minimize labor costs. Suppose that a particular Wal-Mart faces the following constraints:
• Full-time workers supervise part-time workers. In particular at least one full-time hour is needed for every four part-time hours.
• Each worker (whether full-time or part-time) can serve 25 customers per hour, and the store must be able to serve at least 1,000 customers.

Type the following sentences, deleting the blanks and replacing them with numbers (rounding all numbers to the nearest integer):

“In order to minimize labor costs, the Wal-Mart should hire _____ hours of full-time workers and ______ hours of part-time workers. If it makes this choice, its labor costs will be \$_____.”

1. Maximize

W= 4x1 +0x2 – x3

Subject to

x1 + x2+ x3 ≤6

x1 – x2 + x3 ≤10

x1 – x2 – x3 ≤4

x1 ,x2 ,x3 ≥ 0

1. A company manufactures three products X,Y and Z. Each product requires machine time and finishing time as shown in the following table:

Machine time                                     Finishing time

 x 1 hr. 4 hr. y 2hr. 4 hr. z 3hr. 8 hr.

The numbers of hours of machine time and finishing time available per month are 900 and 5000, respectively. The unit profit on X,Y, and Z is \$6,\$8, and \$12, respectively. What is the maximum profit per month that can be obtained

## Series and Sequences

Phillip received 75 points on a project for school. He can make changes and receive two-tenths of the missing points back. He can do this 10 times. Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Phillip can receive.

## HYPOTHESIS TESTING AND TYPE ERRORS

Answer the following problems showing your work and explaining (or analyzing) your results.

1. Explain Type I and Type II errors. Use an example if needed.
2. Explain a one-tailed and two-tailed test. Use an example if needed.
3. Define the following terms in your own words.
• Null hypothesis
• P-value
• Critical value
• Statistically significant
4. A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis HoÂ and the alternative hypothesis Ha.
5. Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you.
• Write the research hypothesis and the null hypothesis.
• Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error.
• Write a paragraph explaining which error would be more severe, and why.
1. Cough-a-Lot childrenâ€™s cough syrup is supposed to contain 6 ounces of medicine per bottle. However since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with Ïƒ = 0.3 ounces.Â  A quality assurance inspector measures 10 bottles and finds the following (in ounces):
 5.95 6.1 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91

Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?

1. State the hypothesis you will test.
2. Calculate the test statistic.
3. Find the P-value.
4. What is the conclusion?
1. Calculate a Z score when X = 20, Î¼ = 17, and Ïƒ = 3.4.
2. Using a standard normal probabilities table, interpret the results for the Z score in Problem 7.
3. Your babysitter claims that she is underpaid given the current market. Her hourly wage is \$12 per hour. You do some research and discover that the average wage in your area is \$14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not.
4. Tutor O-rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is Î¼ = 350 and Ïƒ = 35. The 100 students who completed the tutoring program had an average score of 385 points. Is the average score of 385 points significant at the 5% level? Is it significant at the 1% level? Explain why or why not.

# A standard normal random variable

a standard normal random variable, compute the following probabilities:

1. P(-1.98<= z <=.49)

2. P(.52<=.z <= 1.22)

True or False

3. A + A’ always equals zero.

4.If the variance equals zero, the values of z must add up to zero (ex. 1,-1,2,-2)

5.The normal distribution curve does not have to be symmetric to zero.

## Mathematics

Consider the following data for assets A and B:

Return A = 10% Return B = 19%; Standard deviation A 3%; standard deviation B 5%; Â Beta A= .6; Beta B = 1.4; Pab = 0.4

a. Calculate the expected return, variance, and beta of a portfolio constructed by investing 1/3 in A and 2/3 in asset B.

b. If only the riskless asset and assets A and B are available find the optimum risky asset portfolio if the risk free rate is 8%.

## A small motor manufacturer makes two types of motors

A small motor manufacturer makes two types of motors, model A and B. The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes 3 hours of wiring, 2 hours of drilling, and 1.5 hours of assembly. Each model B must go through 2 hours of wiring, 1 hour of drilling, and 0.5 hours of assembly. During the next production period, 240 hours of wiring time, 210 hours of drilling, and 120 hours of assembly time is available. Each model A sold yeilds a profit of \$22. Each model B can be sold for a \$15 profit. Assuming that all motors that are assembled can be sold, find the best combination of motors to yield the highest profit.

## Retirement savings plan

1. You are about to set up a new retirement savings account that earns interest at a 3% annual interest rate (APR). You want to make monthly contributions to that account from now until you retire in 20 yrs. The goal is to save enough money so that you will be able to withdraw the money you need each month without depleting your principal (in reality, you will probably deplete your principal gradually). How much money do you need to contribute to the account each month if you want to withdraw \$4000 a month?
2.

1. Consider the savings plan you developed in the discussion.Â  How much did you determine you need to save each month?Â  You do not need to repeat those calculations here, but just re-state your conclusion.
2. With the 3% account, the monthly payments might be difficult to maintain, so you decide to wait 5 more years until you retire.Â  What are your monthly payments with this plan?
3. Suppose you can find an account that earns interest at 4% interest instead.Â  How does that change your monthly payments?Â  (You choose how long until you retire in this question.)

Please write out steps taken to get to the solution. Need this as soon as possible. Thanks

## Math Statistics 300

The vast majority of the world uses a 95% confidence in building confidence intervals.Â  Give your opinion on why 95% confidence is so commonplace. Justify your response.

## Bottling Company Case Study

Imagine you are a manager at a major bottling company. Customers have begun to complain that the bottles of the brand of soda produced in your company contain less than the advertised sixteen (16) ounces of product. Your boss wants to solve the problem at hand and has asked you to investigate. You have your employees pull thirty (30) bottles off the line at random from all the shifts at the bottling plant. You ask your employees to measure the amount of soda there is in each bottle. Note: Use the data set provided by your instructor to complete this assignment.

 Bottle Number Ounces Bottle Number Ounces Bottle Number Ounces 1 14.5 11 15 21 14.1 2 14.6 12 15.1 22 14.2 3 14.7 13 15 23 14 4 14.8 14 14.4 24 14.9 5 14.9 15 15.8 25 14.7 6 15.3 16 14 26 14.5 7 14.9 17 16 27 14.6 8 15.5 18 16.1 28 14.8 9 14.8 19 15.8 29 14.8 10 15.2 20 14.5 30 14.6

Write a two to three (2-3) page report in which you:

1. Calculate the mean, median, and standard deviation for ounces in the bottles.
2. Construct a 95% Confidence Interval for the ounces in the bottles.
3. Conduct a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Clearly state the logic of your test, the calculations, and the conclusion of your test.
4. Provide the following discussion based on the conclusion of your test:
1. If you conclude that there are less than sixteen (16) ounces in a bottle of soda, speculate on three (3) possible causes. Next, suggest the strategies to avoid the deficit in the future.

Or

1. If you conclude that the claim of less soda per bottle is not supported or justified, provide a detailed explanation to your boss about the situation. Include your speculation on the reason(s) behind the claim, and recommend one (1) strategy geared toward mitigating this issue in the future.

Your assignment must follow these formatting requirements:

• Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides. Â No citations and references are required, but if you use them, they must follow APA format. Check with your professor for any additional instructions.
• Include a cover page containing the title of the assignment, the studentâ€™s name, the professorâ€™s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.

## Statistics

Homework assignment covers Estimates and Sample Sizes and important concepts for estimating an interval that will contain the true population mean, population proportion and population variance.

Assignemnt attached.

## math homework 15 questions

I have a math homework 15 questions and I post pictures of the homework number the first 3 pages are (25,27,29,35,37,43,49,51,59,63)

and and last 2 pages are ( 7,11,15,25,27)

## probability

The mathematical expression of probability as a number between 0 and 1 is fundamental to understanding statistics. For example, research articles will include a p-value expression such as â€œsignificance less than 0.001. This means that a probability of .001 (equivalent to 1/1000) corresponds to an event so rare that it occurs an average of only once in a thousand trials.

Define and interpret the rare event rule for inferential statistics. This means that you should summarize from the text and then provide your own understanding of the rare event rule. Find an article from a peer-reviewed journal that states the p-value. What is the p-value? What does the p-value tell us? What is the author’s conclusion based on that probability? Was their finding â€œunusualâ€, if unusual is defined as p < .05? Explain.

## Differential Geometry/Calculus of Variations

Do all the problems. I will give you notes we did in class.Thanks

## Statistical Thinking in Health Care

Case Study 1: Statistical Thinking in Health Care
Read the following case study.
Ben Davis had just completed an intensive course in Statistical Thinking for Business Improvement, which was offered to all employees of a large health maintenance organization. There was no time to celebrate, however, because he was already under a lot of pressure. Ben works as a pharmacist’s assistant in the HMO’s pharmacy, and his manager, Juan de Pacotilla, was about to be fired. Juan’s dismissal appeared to be imminent due to numerous complaints and even a few lawsuits over inaccurate prescriptions. Juan now was asking Ben for his assistance in trying to resolve the problem, preferably yesterday!
“Ben, I really need your help! If I can’t show some major improvement or at least a solid plan by next month, I’m history.”
“I’ll be glad to help, Juan, but what can I do? I’m just a pharmacist’s assistant.”
“I don’t care what your job title is; I think you’re just the person who can get this done. I realize I’ve been too far removed from day-to-day operations in the pharmacy, but you work there every day. You’re in a much better position to find out how to fix the problem. Just tell me what to do, and I’ll do it.”
“But what about the statistical consultant you hired to analyze the data on inaccurate prescriptions?”
“Ben, to be honest, I’m really disappointed with that guy. He has spent two weeks trying to come up with a new modeling approach to predict weekly inaccurate prescriptions. I tried to explain to him that I don’t want to predict the mistakes, I want to eliminate them! I don’t think I got through, however, because he said we need a month of additional data to verify the model, and then he can apply a new method he just read about in a journal to identify ‘change points in the time series,’ whatever that means. But get this, he will only identify the change points and send me a list; he says it’s my job to figure out what they mean and how to respond. I don’t know much about statistics — the only thing I remember from my course in college is that it was the worst course I ever took– but I’m becoming convinced that it actually doesn’t have much to offer in solving real problems. You’ve just gone through this statistical thinking course, though, so maybe you can see something I can’t. To me, statistical thinking sounds like an oxymoron. I realize it’s a long shot, but I was hoping you could use this as the project you need to officially complete the course.”
“I see your point, Juan. I felt the same way, too. This course was interesting, though, because it didn’t focus on crunching numbers. I have some ideas about how we can approach making improvements in prescription accuracy, and I think this would be a great project. We may not be able to solve it ourselves, however. As you know, there is a lot of finger-pointing going on; the pharmacists blame sloppy handwriting and incomplete instructions from doctors for the problem; doctors blame pharmacy assistants like me who actually do most of the computer entry of the prescriptions, claiming that we are incompetent; and the assistants tend to blame the pharmacists for assuming too much about our knowledge of medical terminology, brand names, known drug interactions, and so on.”
“It sounds like there’s no hope, Ben!”
“I wouldn’t say that at all, Juan. It’s just that there may be no quick fix we can do by ourselves in the pharmacy. Let me explain how I’m thinking about this and how I would propose attacking the problem using what I just learned in the statistical thinking course.”
Source: G. C. Britz, D. W. Emerling, L. B. Hare, R. W. Hoerl, & J. E. Shade. “How to Teach Others to Apply Statistical Thinking.” Quality Progress (June 1997): 67–80.
Assuming the role of Ben Davis, write a three to four (3-4) page paper in which you apply the approach discussed in the textbook to this problem. You’ll have to make some assumptions about the processes used by the HMO pharmacy. Also, please use the Internet and / or Strayer LRC to research articles on common problems or errors that pharmacies face. Your paper should address the following points:

1. Develop a process map about the prescription filling process for HMO’s pharmacy, in which you specify the key problems that the HMO’s pharmacy might be experiencing. Next, use the supplier, input, process steps, output, and customer (SIPOC) model to analyze the HMO pharmacy’s business process.
2. Analyze the process map and SIPOC model to identify possible main root causes of the problems. Next, categorize whether the main root causes of the problem are special causes or common causes. Provide a rationale for your response.
3. Suggest the main tools that you would use and the data that you would collect in order to analyze the business process and correct the problem. Justify your response.
4. Propose one (1) solution to the HMO pharmacy’s on-going problem(s) and propose one (1) strategy to measure the aforementioned solution. Provide a rationale for your response.
5. Use at least two (2) quality references. Note: Wikipedia and other Websites do not qualify as academic resources.

Your assignment must follow these formatting requirements:

• Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA format. Check with your professor for any additional instructions.
• Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.

The specific course learning outcomes associated with this assignment are:

• Describe how organizations use statistical thinking to be more competitive.
• Apply the basic principles of statistical thinking to business processes.
• Apply the SIPOC model to identify OFIs in business processes.
• Use technology and information resources to research issues in business process improvement.
• Write clearly and concisely about business process improvement using proper writing mechanics.

Thoughts on the Case Study

1. Develop a process map about the prescription filling process for HMO’s pharmacy, in which you specify the key problems that the HMO’s pharmacy might be experiencing. Next, use the supplier, input, process steps, output, and customer (SIPOC) model to analyze the HMO pharmacy’s business process.

In this paragraph, you may find out what is the pharmacy medication dispense process. In your pharmacy, please identify your supplier (S), input (I), process (P), output (O) and customers (C). Once you map out the process, you may identify some potential errors, you ca also make suggestions on how you can take proper data to improve the process.

There are many references you may find on the Internet. Some examples include
http://www.thinkreliability.com/hc-medicationerror.aspx
http://tdapharm.hubpages.com/hub/How-are-Medications-Filled-in-a-Pharmacy

You may also get additional information on pharmacy operations in the reference PowerPoint file.

1. Analyze the process map and SIPOC model to identify possible main root causes of the problems. Next, categorize whether the main root causes of the problem are special causes or common causes. Provide a rationale for your response.

Please describe some most likely root cause(s) of errors or customer complaints (Pick top 3 causes). Please discuss if those causes are common cause or special causes in the process. Please discuss the reasons for your causes.

1. Suggest the main tools that you would use and the data that you would collect in order to analyze the business process and correct the problem. Justify your response.

Please discuss the tools (knowledge tools, subject matter expert opinions, data collections or numerical tools etc.) you would recommend that may help you identify the root causes or solve the customer complaints. Please note the practical limitation of the recommended tools.

1. Propose one (1) solution to the HMO pharmacy’s on-going problem(s) and propose one (1) strategy to measure the aforementioned solution. Provide a rationale for your response.

In this paragraph, please provide at least one problem-solving approach for the HMO pharmacy. Please clearly identify what is the problem you are solving in the approach? How would you solve it? How do you know (measure) your success or effectiveness?

1. Use at least two (2) quality references. Note: Wikipedia and other Websites do not qualify as academic resources.

## Linear Programming Case Study

Assignment 1. Linear Programming Case Study
Your instructor will assign a linear programming project for this assignment according to the following specifications.
It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it wonâ€™t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.
You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.
Writeup.
Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.
Excel.
As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.

## Sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was:

## Statistics Assignment

Â
Name:______________________________________
Â
Module 2 Homework Assignment

• 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.

• Find the critical value for zÎ±/2 that corresponds to a degree of confidence of 98%.

• Find the critical value for tÎ±/2 corresponding to n = 12 and 95% confidence level.

• Use the confidence level and sample data to find the margin of error E.

College studentsâ€™ annual earnings:
99% confidence, n = 74, = \$3967, s = \$874

• Construct the confidence interval for question 4 above.

• Write a statement that correctly interprets the confidence interval found in question 5.

• Find the critical value corresponding to a sample size of 19 and a confidence level of 99%.

• Find the critical value corresponding to a sample size of 19 and a confidence level of 99%.

• The values listed below are the waiting times (in minutes) of customers at the Bank of Providence, where customers enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation and write a statement that correctly interprets the results.

4.2Â Â Â Â Â Â Â Â Â  5.4Â Â Â Â Â Â Â Â Â  5.8Â Â Â Â Â Â Â Â Â  6.2Â Â Â Â Â Â Â Â Â  6.7Â Â Â Â Â Â Â Â Â  7.7Â Â Â Â Â Â Â Â Â  8.5Â Â Â Â Â Â Â Â Â  9.3Â Â Â Â Â Â Â Â Â  10.0

• You want to estimate s for the population of waiting times at a fast-food restaurantâ€™s drive-up windows, and you want to be 95% confident that the sample standard deviation is within 20% of s. Find the minimum sample size needed. Is this sample size practical?

## statistics phase2

This week you will begin working on Phase 2 of your course project. Using the same data set and variables for your selected topic, add the following information to your analysis:

1. Discuss the importance of constructing confidence intervals for the population mean.
• What are confidence intervals?
• What is a point estimate?
• What is the best point estimate for the population mean? Explain.
• Why do we need confidence intervals?
1. Based on your selected topic, evaluate the following:
• Find the best point estimate of the population mean.
• Construct aÂ 95%Â confidence interval for the population mean. Assume that your data is normally distributed and ÃƒÃ†â€™ is unknown.
• Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.
• Write a statement that correctly interprets the confidence interval in context of your selected topic.
1. Based on your selected topic, evaluate the following:
• Find the best point estimate of the population mean.
• Construct aÂ 99%Â confidence interval for the population mean. Assume that your data is normally distributed and ÃƒÃ†â€™ is unknown.
• Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.
• Write a statement that correctly interprets the confidence interval in context of your selected topic.
1. Compare and contrast your findings for the 95% and 99% confidence interval.
• Did you notice any changes in your interval estimate? Explain.
• What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain.

## W4 Finite Mathematics Midterm

### Question 1

Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope – 1.
 A. B. C. D.

### Question 2

 A. B. C. D. No solution

### Question 3

 A. x = 16, y = 0, z = 16, t = 0, u = 80, v = 21, w = 61, P = 180 B. x = 0, y = 16, z = 0, t = 0, u = 80, v = 21, w = 61, P = 96 C. x = 80, y = 16, z = 0, t = 0, u = 0, v = 21, w = 61, P = 68 D. x = 80, y = 0, z = 0, t = 16, u = 80, v = 21, w = 61, P = 174

### Question 4

 A. B. C. D.

### Question 5

 A. B. C. D. No solution

### Question 6

 A. B. C. D. No solution

### Question 7

 A. B. C. D.

### Question 8

 A. B. C. D. E.

### Question 9

 A. B. C. D. infinitely many solutions E. no solution

### Question 10

Metro Department Store’s annual sales (in millions of dollars) during 5 years were

 Annual Sales, y 5.8 6.1 7.2 8.3 9 Year, x 1 2 3 4 5

Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

 A. B. C.

### Question 11

If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?
 A. a = -8 B. a = 4 C. a = -4 D. a = 8

### Question 12

 A. B. C. D.

### Question 13

 A. B. C. D. E. y is not a linear function of x.

### Question 14

 A. B. C. D. E.

### Question 15

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9
 A. B. C. D. E. y is not a linear function of x.

### Question 16

 A. ( 0, 2 ) B. ( 8, 2 ) C. ( 4, â€“6 ) D. ( â€“2, 4 ) E. ( 4, â€“2 )

### Question 17

 A. The matrix is in row-reduced form. B. The matrix is not in row-reduced form.

### Question 18

 A. B. C. D. E.

### Question 19

 A. B. C. D. E.

### Question 20

Find the slope of the line that passes through the given pair of points.
(2, 2) and (8, 5)
 A. B. C. D. E.

### Question 21

 A. ( 7, â€“3 ) B. ( 6, â€“2 ) C. ( 2, â€“6 ) D. ( â€“6, 2 ) E. ( â€“7, â€“2 )

### Question 22

 A. B. C. D. E.

### Question 23

 A. B. C. D. E.

### Question 24

 A. B. C. D. E.

### Question 25

Find an equation of the line that passes through the points (1, 4) and ( -7, -4)
 A. y = 7x + 7 B. y = x + 3 C. y = 3x – 7 D. y = 3x – 3

## G180 Module 08 Assignment

G180 Module 08 Assignment

1. Looking at the above graph, identify the number of odd vertices.

1. Looking at the above graph, identify the number of even vertices.

1. Looking at the above graph. Does it have an Euler circuit? Does it have an Euler path? Explain your answers.

1. Which of the above graphs has an Euler circuit?

1. Which of the above graphs has an Euler path but no Euler Circuit?

## Algorithm

Fleury’s algorithm is a way to explain how to find an Euler circuit or Euler path. An algorithm, in general, is a method or procedure that one can use to determine a solution to a problem. But an algorithm can be used to solve real world problems, as well, such as to make a sandwich.
Create your own algorithm (procedure) to make a sandwich and share it here. Then, explain why your procedure is the one you chose

## Statistics 2

You are expected to demonstrate critical thinking and your understanding of the content in the assigned readings as they relate to the issues identified in the conference discussion. Please make your own contribution in a main topicÂ byÂ 11:59 PM ET on ThursdaysÂ as well as respond with value-added comments to your classmate byÂ 11:59 PM ET on Sundays. When posting a main topic, please start a new thread and put the discussion topics there.Â Two substantive contributions (one main topic and one response)Â are required to get the weekly points of credit for Weekly conference. Late postings are not accepted.
Please choose one of the following topics as your main topic postingÂ for Week 2:
(1) What statistical measure do you use / see most often?
(2) Why does the Census Bureau publish the median household income? Why shouldn’t the Bureau publish the mean household income?
(3) If you are told that the variance of a data set is 0, what conclusion can you make about the observations in the data set? Why?

## Measures of Central Tendency

This require 3 different answers/papers, please pay attention to the attachments since it is a follow on question to a previous assignment (SLP PORTION).

You will need to create a chart for SLP 1 in order to complete SLP 2, SLP 1 is in the attachments as (working Copy).
PART 1

CASE

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

1.Â Â Â  Describe the measures of central tendency. Under what condition(s) should each one be used?

2.Â Â Â  Last year, 12 employees from a computer company retired. Their ages at retirement are listed below. First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year.

55Â Â Â 77Â Â Â 64Â Â Â 77Â Â Â 69Â Â Â 63Â Â Â 62Â Â Â 64Â Â Â 85Â Â Â 64Â Â Â 56Â Â Â 59

1. A retail store manager kept track of the number of car magazines sold each week over a 10-week period. The results are shown below.
27Â Â Â 30Â Â Â 21Â Â Â 62Â Â Â 28Â Â Â 18Â Â Â 23Â Â Â 22Â Â Â 26Â Â Â 28

1. Find the mean, median, and mode of newspapers sold over the 10-week period.
2. Which measure(s) of central tendency best represent the data?
3. Name any outliers.

1. Joe wants to pass his statistics class with at least a 75%. His prior four test scores are 74%, 68%, 84% and 79%. What is the minimum score he needs on the final exam to pass the class with a 75% average?
2. Nancy participated in a summer reading program. The number of books read by the 23 participants are as follows:
10Â Â Â Â 9Â Â Â Â 6Â Â Â Â 2Â Â Â Â 5Â Â Â Â 3Â Â Â Â 9Â Â Â Â 1Â Â Â Â 6Â Â Â Â 3Â Â Â Â 10Â Â Â Â 4Â Â Â Â 7Â Â Â Â 6Â Â Â Â 3Â Â Â Â 5Â Â Â Â 6Â Â Â Â 2Â Â Â Â 6Â Â Â Â 5Â Â Â Â 3Â Â Â Â 7Â Â Â Â 2

 Number of books read Frequency 1â€“2 3â€“4 5â€“6 7â€“8 9â€“10

1. Complete the frequency table.
2. Find the mean of the raw data.
3. Find the median of the raw data.

1. The chart below represents the number of inches of snow for a seven-day period.

 Sunday Monday Tuesday Wednesday Thursday Friday Saturday 2 5 3 10 0 4 2

1. Find the mean, median, and mode.
2. Which is the best measure of central tendency?
3. Remove Wednesday from the calculations. How does that impact the three measures of central tendency?
4. Describe the effect outliers have on the measures of central tendency.

1. A dealership sold 15 cars last month. The purchase price of the cars, rounded to the nearest thousand, is represented in the table.

 Purchase price Number of cars sold \$15,000 3 \$20,000 4 \$23,000 5 \$25,000 2 \$45,000 1

1. Find the mean and median of the data.
2. Which measure best represents the data? Use the results to support your answer.
3. What is the outlier and how does it affect the data?
8. What do the letters represent on the box plot?

9. The test scores from a math final exam are as follows:
64Â Â Â 85Â Â Â 93Â Â Â 55Â Â Â 87Â Â Â 90Â Â Â 73Â Â Â 81Â Â Â 86Â Â Â 79

1. Create a box plot using the data.
2. Label the five points on the box plot and include numerical answers from part “a.”
10. Using the data and results from Question 9, answer the following questions.

1. What is the median?
2. What is the range?
3. What is the interquartile range?
4. In a short paragraph, describe the data in the box plot.

PART 2:
SLP

Â Using the data you collected in the Module 1 SLP, write a paper (1â€“3 pages) including all of the following content:

• Calculate the mean, median, and mode of your collected data. Show and explain your calculations.
• Are these numbers higher or lower than you expected? Explain.
• Which of these measures of central tendency do you think most accurately describes the variable you are looking at? Provide your justification.
• Create a box plot to represent the data, labeling and numerating all 5 points on the box plot. For the plot, you may draw and insert it in your paper as a picture. Make sure it is legible.
Submit your paper at the end of Module 2.
SLP Assignment Expectations
Answer all questions posted in the instructions. Use information from the modular background readings and videos as well as any good-quality resource you can find. Cite all sources in APA style and include a reference list at the end of your paper.
Note about page length: Your ability to clearly articulate and explain these concepts is being assessed. The page length is a general guideline. A 3- or 4-page paper does not necessarily guarantee a grade of â€œA.â€ An â€œAâ€ paper would include detailed information and explanations of all the assignment requirements listed above. The letter grade will be based upon demonstrated mastery of the content and ability to articulate and apply the concepts in the assignment. Keep this in mind while writing your paper.
PART 3:
• Measure of Central Tendency

In the business world, the mean salary is often used to describe the salaries of employees of a company. However, the median salary may be a better measure of the salaries than the mean. Which is the better measure of central tendency? Why? Review and respond to the comments posted by your classmates offering your insight on this topic.

## Statistics

What are examples of variables that follow a binomial probability distribution? What are examples of variables that follow a Poisson distribution? When might you use a geometric probability?

## "t" test for independent means

I would like to do my paper on drug addiction. I would like to research the difference between those who seek treatment with drug replacement therapy vs. those who do not use drug replacement therapy.
Pay particular attention to the information on the “t” test for independent means

I need the math work incorporated into my already written paper. There is a sample paper attached this is what mine needs to be like. I also attached my paper that is already written just needs the math incorporated into it. This is what I need you to do (incorporate the problem into the paper). Also attached is the numbers to be used for the statistical math problem.

## Statistics

### QuestionÂ 1

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The line described by aÂ regression equationÂ attempts to:
Select one:
a.Â pass through as few points as possible.
b.Â pass through as many points as possible.
c.Â minimise the total squared distances from the points.
d.Â minimise the number of points it touches.

### QuestionÂ 2

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A regression analysis isÂ inappropriateÂ when:
Select one:
a.Â You want to make predictions for one variable based on information from another variable.
b.Â You have two numerical variables.
c.Â The pattern of points in the scatterplot forms a reasonably straight line.
d.Â There is a pattern in the plot of residuals versus fitted values.

### QuestionÂ 3

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If theÂ slopeÂ of a regression line is equal to 2.00, this implies:
Select one:
a.Â For every increase of 2.00 on theÂ x-axis theÂ y-axis value is halved.
b.Â For every increase of 2.00 on theÂ x-axis there is an increase of 2.00 on theÂ y-axis.
c.Â For every increase of 1.00 on theÂ x-axis there is an increase of 2.00 on theÂ y-axis.
d.Â Very little.

### QuestionÂ 4

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When testing a linear relation, what are the appropriateÂ null and alternate hypotheses?
Select one:
a.Â H0: Î² = 0,Â Â H1: Î² â‰  0
b.Â H0: Î² â‰ Â 0,Â Â H1: Î² = 0
c.Â H0: bÂ â‰ Â 0,Â Â H1: b = 0
d.Â H0:Â ÂµÂ = 0,Â Â H1: Âµ â‰  0
e.Â H0: b = 0,Â Â H1: b â‰  0
f.Â H0:Â Î±Â = 0,Â Â H1:Â Î±Â â‰  0

### QuestionÂ 5

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Match anyÂ trendsÂ in the scatter plots with the most appropriate descriptions:
 Answer 1Choose…Strong negative relationshipWeak negative relationshipWeak positive relationshipStrong positive relationshipNo relationship Answer 2Choose…Strong negative relationshipWeak negative relationshipWeak positive relationshipStrong positive relationshipNo relationship Answer 3Choose…Strong negative relationshipWeak negative relationshipWeak positive relationshipStrong positive relationshipNo relationship

### QuestionÂ 6

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For the plots above regarding a regression of the percentage of potato chips broken on the percentage of potato content, are all theÂ assumptionsÂ met? Select the best answer.
Select one:
a. No, the relation does not look linear
b. No, the residuals are not evenly spread either side of the horizontal line for the range of x-values
c.Â None of the assumptions appear to be satisfied.
d. No, the histogram of the residuals is not sufficiently symmetric
e. Yes

### QuestionÂ 7

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The regression goodness-of-fit,Â r2, tells us:
Select one:
a.Â The proportion of variability in y accounted for by x.
b.Â All of the above.
c.Â How to determine someone’s score.
d.Â How to describe a relationship.

### QuestionÂ 8

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Which of the following hypotheses could be tested using aÂ chi-square goodness-of-fit test?
Select one:
a.Â Choice of car colour is directly related to measures of extroversion.
b.Â None of the other choices.
c.Â Individuals with red cars are significantly more extroverted than individuals with green, black or silver cars.
d.Â In terms of car colour, more individuals choose a red car, than a green, a black or a silver car.

### QuestionÂ 9

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#### Question text

In a chi-square test of independence, theÂ degrees of freedomÂ for a table with 9 rows and 8 columns will be:

### QuestionÂ 10

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#### Question text

Predicting Percentage of Chips Broken:
Regression Analysis: %Broken chips versus %Potato
The regression equation is
%Broken chips =Â 7.93 – 0.151 %Potato
Predictor Â  Â  Coef Â SE Coef Â  Â  T Â  Â  P
Constant Â  Â 7.9301 Â  0.5225 15.18 0.000
%Potato Â  -0.15084 Â 0.05912 _____ 0.012
S = 2.03470 R-Sq = 6.2% R-Sq(adj) = 5.3%

The Minitab output above is from a regression of the percentage of potato chips broken versus the percentage of potato content in those chips. Use the output to answer the following questions.

1. What is the value of a?Â Â (1 dp) Â Â Answer
2. What is the value of b?Â Â (4 dp) Â Â Answer
3. What is the se(b)?Â Â (4dp) Â Â Answer
4. Calculate the absolute value of the test statistic for b.Â Â (2dp) Â Â Answer
5. What is the goodness of fitÂ  (as a percentage)?Â (1 dp) Â Â Answer
6. What is the correlation?Â Â (2 dp)Â Â Â Answer
7. Would youÂ (A)Â reject orÂ (B)Â not reject the hypothesis thatÂ Â Â ?Â Â Â Answer

## NEED ENTIRE COURSE COMPLETED

I AM IN NEED OF SOMEONE Â who will do my ENTIRE 8 WEEK COURSE in MTH4101. I am willing to pay for the entire 8 weeks, 1/2 up front and the rest at completion. I am entirely UNEQUIPPED to do math of any kind.

## Sequences and Series

1. Denise is designing the seating arrangement for a concert an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the first row can only have 11 seats. Help Denise plan the rest of the seating by solving for how many seats are in row 18. Then explain to Denise how to create an equation to predict the number of seats in any row. Show your work, and use complete sentences.
2.Â Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) = 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x â€“ 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done.
3.Â Brian has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.17 times as many villagers. The game gave Brian 8 villagers to start with. Help Brian expand his empire by solving for how many villagers he can create with 16 towns. Then explain to Brian how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.
4.Â Christina has some money at home, and the amount is modeled by the function h(x) = 103. She read about a bank that has savings accounts that accrue interest according to the function s(x) = (1.03)x â€“ 1. Using complete sentences, explain to Christina how she can combine her functions to create a new function, and explain what this new function means.
5.Â Phillip received 75 points on a project for school. He can make changes and receive two-tenths of the missing points back. He can do this 10 times. Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Phillip can receive.

## Algebra 1 Homework Problems

Algebra 1 Homework Problems:
Here is the link to the text book for the page numbers and problems
http://ocas.pearsonschool.com/ph/cd/0-13-365946-8/index.html?pageid=750&token=53616c7465645f5f81d8086b402612535c05bb36548c352efd4d42aa1f0bb0bdac910c59b0106743211d5f73e68757a01aa7c21cd8986203d225aa23afe42a72ef07f866009a4e4b

 Â Page and Problems DATA ANALYSIS & PROBABILITY Organizing Data Using Matrices P. 717-718 #9, 11, 15, 17.. Frequency and Histograms P. 723-724 #7, 9, 11, 15, 17. Measures of Central Tendency P. 730-731 #7, 9, 11, 17. Box and Whisker Plots P. 738 #9, 11, 13, 15, 21 Samples and Surveys P. 744-745 #7, 9, 15, 17, 19, 21 Permutations & Combinations P. 754-755 #15, 17, 19, 25, 27, 29, 37,39. Theoretical & Experimental Probability P. 761-762 #11, 13, 23, 25, 29, 31. Probability of Compound Events P. 768-769 #11, 13,17,19,21,25. EXPONENTS AND EXPONENTIAL FUNCTIONS Zero & Negative Exponents P. 417-418 #11, 13, 15,17,21,23,29,33. Scientific Notation P. 424 #11, 13, 19, 23, 35. Multiplying Powers with Same Base P. 429-430 #9,11,15,17,21. More Multiplication Properties of Exponents P. 436-437 #11,15,17,31,33. Division Properties of Exponents P. 444 #9, 11, 13, 21. Exponential Functions P. 450-451 #9, 15, 21. Exponential Growth & Decay P. 459-460 #9, 11, 15, 29, POLYNOMIALS AND FACTORING Adding & Subtracting Polynomials P. 477 #9, 11, 13 P. 477 #17, 19, 21, 31 Multiplying & Factoring Polynomials P. 483 #9, 11, 15, 19 P. 484 #21, 25, 27, 31 Multiplying Binomials P. 489 #9, 11, 13 P. 490 #21, 23, 25, 31 Multiplying Special Cases P. 495-497 #9, 11, 17, 21, 27. Factoring x^2 + bx + c P. 503-505 #11, 13, 15, 17, 25, 27. Factoring ax^2 + bx + c P. 508-509 #11, 13, 15. Factoring Special Cases P. 514-515 #9, 11, 17, 19, 23. Factoring by Grouping P. 519-521 #13, 15, 17, and 29.

 Quadratic Graphs & Their Properties P. 538-539 #7, 9, 17, 21. Quadratic Functions P. 544-545 #7, 9, 11, 21. Solving Quadratic Equations P. 551-553 #11, 13, 21, 23, 27. Completing the Square P. 564-565 #13, 15, 19, 31. Quadratic Formula & The Discriminant P. 571-572 #7, 9, 11, 13, 23, 27. Linear, Quadratic, Exponential Models P. 578-579 #7, 13, 15. Systems of Linear & Quadratic Equations P. 585-586 #9, 11, 15, 19. RADICAL EXPRESSIONS & EQUATIONS The Pythagorean Theorem P. 603 #7, 11, 13, 23. Simplifying Radicals P. 610-612 #11, 13, 15, 23, 27 P. 610-612 #37, 39, 54 Operations with Radical Expressions P. 616-618 #9, 13, 19, 23, 25 P. 616-618 #39, 41, 49 Trigonometric Ratios P. 637-638 #9, 13, 16, 25, 27, 29. RATIONAL EXPRESSIONS & FUNCTIONS Simplifying Rational Expressions P. 655-656 #9, 15, 19, 25. Multiplying & Dividing Rational Expressions P. 662 #11, 15, 19, 27 P. 662 #33, 37, 39

## Algebra Problems

Please look over each problem to see if it makes sense to you prior to bidding. Thank you.

One: If F(x)=3xâˆ’âˆ£3+xâˆ£, find F(4) and F(âˆ’4).
F(4)= ____________
F(âˆ’ 4)= ____________

Two: If f(x)=6x2âˆ’4x, find f(2+z).
Enter the expression in simplest form. The terms of the expression must be entered in descending order of degree.
f(2+z)= __________

Three (steps for this would be great) : If
w(x)=
4Â Â Â Â Â Â Â Â Â Â Â Â Â  ifxâ‰¤âˆ’8
âˆ£4xâˆ’4âˆ£Â Â Â  ifâˆ’8<x<3
4x+4Â Â Â Â Â  ifxâ‰¥3
find w(3) and w(âˆ’10).
w(3)= ____________
w(âˆ’10)= ____________

 Â

Four: Write the domain and range of the function using interval notation.
(a) Write the domain

 (a) (âˆ’2,3] (b) [âˆ’2,3) (c) [3,8) (d) R (e) [3,8] (f) [âˆ’1,8]
(b) Write the range

 (a) R (b) (3,8) (c) [âˆ’1,8] (d) [3,8] (e) (âˆ’2,3) (f) [âˆ’2,3]

five: Using the graph, find f(0) and find x such that f(x)=âˆ’2.
f(0)= ____________Â Â Â  and f(x)=âˆ’2 when x= ____________

Six:: Given w(t)=6+7t^2 and g(t)=7tâˆ’6, find (wg)(t).
Enter the expression in simplest form.
(wg)(t)= __________

Seven: Given s(x)=âˆ’2x^2 and w(x)=3x+3, find (s w)(0).
(s w) (0)= __________

Eight: Find (w âˆ˜ g)(1) for w(x)=7x^2âˆ’2x+8 and g(x)=2xâˆ’7.
(w âˆ˜ g) (1)= ____________
Nine: Find (p âˆ˜ p) (âˆ’1) for p(x)=3x^2+2xâˆ’3.
(p âˆ˜ p) (âˆ’1)= ____________
Ten: A car dealership offers a \$1,500 factory rebate and a 9% discount off the price of a new car c.
Write a functionr for the cost of the car after receiving only the factory rebate.
r(c)= c+1,500 [Â Â ]Â Â câˆ’1,500 [Â Â ]Â Â 1,500c [Â Â ]Â Â c/1,500 [Â Â ]
Write a function p for the cost of the car after receiving only the dealership discount.
p(c)= câˆ’9 [Â Â ]Â Â câˆ’0.09 [Â Â ]Â Â 0.09c [Â Â ]Â Â 0.91c [Â Â ]
Evaluate (râˆ˜p)(c) and explain what the composition represents.
(râˆ˜p)(c)= 0.91câˆ’1,500 [Â Â ]Â Â 0.09câˆ’1,500 [Â Â ]Â Â 0.91câˆ’1,365 [Â Â ]Â Â 0.91c+1,365 [Â Â ]
(râˆ˜p)(c) represents the cost of the car when the __________ is applied first and then the __________ is applied.

## Correlation & Regression

Correlation

1. What results in your departments seem to be correlated or related (either causal or not) to other activities?
2. How could you verify this?
3. What are the managerial implications of a correlation between these variables?

Regression
At times we can generate a regression equation to explain outcomes.Â  For example, an employeeâ€™s salary can often be explained by their pay grade, appraisal rating, education level, etc.
1. What variables might explain or predict an outcome in your department or life?
2. If you generated a regression equation, how would you interpret it and the residuals from it

## Regression Testing

Can someone help me with this assignment
1.
In a regression model with one independent variable X, the intercept or constant (b0) represents the

1. A) predicted value of the dependent variable Y when the X = 0.
2. B) estimated average per unit change in the dependent variable for every unit change in X.
3. C) predicted or fitted value of dependent variable.
4. D) Average variation around the sample regression line.

2.
In a regression model with one independent variable X, the slope coefficient (b1) represents the

1. A) predicted value of the dependent variable Y when the X = 0.
2. B) estimated average per unit change in the dependent variable for every unit change in X.
3. C) predicted or fitted value of dependent variable.
4. D) average variation around the sample regression line.

3.
If one examines the relationship between two variables, the correlation (r) and the slope coefficient (b1) in a simple regression model

1. A) may have opposite signs.
2. B) must have the same signs.
3. C) must have opposite signs.
4. D) are equal.

4.
If one examines the relationship between two variables, the correlation (r) and the slope coefficient (b1) in a multiple regression model

1. A) may have opposite signs.
2. B) must have the same signs.
3. C) must have opposite signs.
4. D) are equal.

5.
Suppose you were given data on number of radio ads and sales for a local department store. You had observations for 20 months. The correlation between ads and sales is 0.40. Does this indicate a positive and significant relationship between ads and sales at the 0.005 level of significance?

1. A) Yes
2. B) No
3. C) Not enough information to determine significance

6.
R2 detects the strength of the relationship between the dependent variable and any individual independent variable.

1. A) True
2. B) False

7.
When an explanatory variable is dropped from a multiple regression model, R2 can increase.

1. A) True
2. B) False

8.
If one tests to see if the value of R-squared is statistically different from zero, one should use a

1. A) t-statistic.
2. B) F-statistic.
3. C) z-statistic.
4. D) correlation coefficient (r).

9.
In a multiple regression model, the adjusted R2

1. A) can be negative.
2. B) must be positive.
3. C) has to be larger than R2.
4. D) can be larger than 1.

10.
In a multiple regression model, the intercept or constant (b0)

1. A) forces the regression line to go through the origin (point where dependent variable is zero when the independent variable is zero).
2. B) is typically unimportant in interpreting the model so can be omitted from model with little effect on results.
3. C) measures the portion of variation in the dependent variable that is explained by the variation in all the independent variables.
4. D) provides flexibility so the least squares method can estimate the best line fit for data in the relevant range of firm operations.

11.
Which of the following is NOT a part of regression specification?

1. A) Selecting the dependent variable.
2. B) Identifying important independent variables.
3. C) Explaining expected signs for the coefficients of each independent variable.
4. D) Forecasting the expected value of R2 for your model.

Situation 7.1.1:
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bankâ€™s charges (Y) — measured in dollars per month — for services rendered to local companies. One independent variable used to predict service charge to a company is the companyâ€™s annual sales revenue (X) — measured in millions of dollars. Data for 21 companies who use the bankâ€™s services were used to fit this model:
(Y) = b0 + b1X
The results of the simple linear regression are provided below.

 Model Variable Coefficient t-statistic (absolute value) B0 Constant -270 1.25 B1 X 200 1.75 R2 = 0.63

12.
Referring to Situation 7.1.1, interpret the estimate of b0.

1. A) All companies will be charged at least \$270 by the bank.
2. B) There is no practical interpretation since bank charges of less than \$0 is a nonsensical value.
3. C) About 95% of the observed service charges fall within \$270 of the least squares line.
4. D) For every \$1 million increase in sales revenue, we expect a service charge to decrease \$2,700.

13.
Referring to Situation 7.1.1, interpret b1 using the appropriate t-test (Hint: first determine whether this should be a one-tail or two-tail test).

1. A) There is insufficient information to determine the statistical significance of sales revenue.
2. B) There is sufficient evidence (at the a = 0.05) to conclude that sales revenue (X) is a significant predictor of service charge (Y).
3. C) There is insufficient evidence (at the a = 0.10) to conclude that sales revenue (X) is a significant predictor of service charge (Y).
4. D) For every \$1 million increase in sales revenue, we expect the service charge to decrease by \$70.

14.
Referring to Situation 7.1.1, what is the percentage of the total variation in bank charges explained by variations in company sales revenue?

1. A) 175%
2. B) 125%
3. C) 95%
4. D) 63%

15.
Referring to Situation 7.1.1, what is the fitted value of bank charges when company sales revenue is \$10m?

1. A) \$1260
2. B) \$1730
3. C) \$2000
4. D) \$6300

Situation 7.1.2:
An economist is interested to see how consumption for an economy (in \$ billions) is influenced by gross domestic product (\$ billions) and aggregate price (consumer price index). The economist used observations from 15 industrialized countries to estimate the relationship. The Microsoft Excel output of this regression is partially reproduced below.

 Variable Coefficient Standard Error Constant -0.086 0.567 GDP 0.765 0.057 Price -0.0006 0.0028 R2 = 0.96; Adjusted R2 = 0.93 F = 18.63

16.
Referring to Situation 7.1.2, one economy in the sample had an aggregate consumption level of \$3 billion, a GDP of \$3.5 billion, and an aggregate price level of 125. What is the residual for this data point?

1. A) \$2.52 billion
2. B) \$0.48 billion
3. C) â€“ \$1.33 billion
4. D) â€“ \$2.52 billion

17.
Which of the independent variables (price, GDP) in Situation 7.1.2 is statistically significant and, therefore, important to explaining variations in consumption (Hint: you are provided standard errors not t-statistics in the table)?

1. A) GDP only
2. B) Price only
3. C) Both GDP and Price
4. D) Neither GDP or Price

18.
Referring to Situation 7.1.2, interpret the test to determine whether the model (all independent variables taken together) have statistically significant explanatory power.

1. A) Since the R2 indicates that variation in all independent variables explain 96% of the variation in the dependent variables, the model can be interpreted as having significant explanatory power.
2. B) Using a = 0.05 and F = 3.59, the null hypothesis is rejected and the model can be interpreted as having significant explanatory power.
3. C) Using a = 0.05 and F2,12 = 3.89, the null hypothesis is rejected and the model can be interpreted as having significant explanatory power.
4. D) Using a = 0.05 and t12 = 1.7823, the null hypothesis is rejected and the model can be interpreted as having significant explanatory power.

19.
The economist in Situation 7.1.2 decided to add a new variable, the percentage of GDP devoted to agriculture, to the model. The new results included an R2 = 0.98 and Adjusted R2 = 0.92. How do you interpret these changes?

1. A) Since R2 increased by more than adjusted R2 decreased, the new variable was an important addition to the model.
2. B) The change in adjusted R2 implies that the benefit of the information added by the new variables is less than the cost in lost degrees of freedom caused by adding the new variable so the new variable is not an important addition to the model.
3. C) One cannot evaluate the importance of the new variable to the model without knowing either the standard error or t-statistic for the variableâ€™s coefficient.

20.
There are several reasons why choices between alternative regression models should NOT be based on which model has the highest R2. Which of the following is NOT one of those reasons?

1. A) Models using time series data will have higher R2 than models using cross-sectional data.
2. B) Some variables are inherently more unstable and thus harder to predict.
3. C) R2 indicates relationships not causality.
4. D) R2 captures the individual effects of variables but not the effects of all variables.