Linda is a half marathon runner. She read an article in a runner’s magazine promoting a new sports beverage that contains protein. She has always used a traditional carbohydrate-rich sports beverage, and has had great results. However, she wonders if this new product would work even better and help her run faster.
Would this new sports beverage containing protein work well for Linda?
        
How much protein should Linda be consuming before and during a half marathon?

Use the AIU Library, magazine, newspaper, or the Internet to research and find a situation where data has been represented by a visual aid and where you believe the visual aid is being used in a manner that evokes emotion or in a manner that misrepresents these data. Note: Some graphics may not be copied and pasted into the DB thread correctly. Please insert your graphics into a Word document and attach the Word document to your DB post so your classmates are able to see your graphics. Discuss the following: Provide your choice of visual data representation displayed to demonstrate your thoughts. Explain in detail how you think the data are visually misrepresented or designed to evoke emotions that may cause someone to make an incorrect decision (and be sure to state which emotions). What types of visual data representations do you find most informative? What about the data representation influences your belief? What type of visual data representation do you think would best display percentage information? Why do you believe this? What type of visual data representation do you think would best represent a comparison of similar data from three different companies (e.g., net annual profit for last year)? Why do you believe this?

A magazine uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers. Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Retailer A and Retailer B customers are shown below.

(a)

Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ₁ = population mean satisfaction score for Retailer A customers and μ₂ = population mean satisfaction score for Retailer B customers.)

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

(b)

Assume that experience with the satisfaction rating scale of the magazine indicates that a population standard deviation of 11 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

At a 0.05 level of significance what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.    Do not Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

(c)

Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Round your answers to two decimal places.)

to

Which retailer, if either, appears to have the greater customer satisfaction?

The 95% confidence interval  ---Select--- is completely below is completely above contains zero. This suggests that the Retailer A has a  ---Select--- higher lower population mean customer satisfaction score than Retailer B.

A magazine published data on the best small firms in a certain year. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the chief executive officers for the first 68 ranked firms.

(a) What is the frequency for CEO ages between (but not including) 54 and 65? (Enter your answer as a whole number.)


(b) What percentage of CEOs are 65 years or older? (Round your answer to the nearest whole number.)
%

(c) What is the relative frequency of ages under 50? (Round your answer to two decimal places.)


(d) What is the cumulative relative frequency for CEOs younger than 55? (Round your answer to two decimal places.)

The publisher of a sports magazine plans to offer new subscribers one of three gifts: a sweatshirt with the logo of their favorite team, a coffee cup with the logo of their favorite team, or a pair of earrings with the logo of their favorite team. In a sample of 500 new subscribers, the number selecting each gift is reported below. At the .05 significance level, is there a preference for the gifts or should we conclude that the gifts are equally well liked?

A magazine uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers. Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Retailer A and Retailer B customers are shown below.

(a)

Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ₁ = population mean satisfaction score for Retailer A customers and μ₂ = population mean satisfaction score for Retailer B customers.)

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

(b)

Assume that experience with the satisfaction rating scale of the magazine indicates that a population standard deviation of 13 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

At a 0.05 level of significance what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.    Do not Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

(c)

Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Round your answers to two decimal places.)

to

Which retailer, if either, appears to have the greater customer satisfaction?

The 95% confidence interval  ---Select--- is completely below contains is completely above zero. This suggests that the Retailer A has a  ---Select--- higher lower population mean customer satisfaction score than Retailer B.

A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a “bar” as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. To convert the data into useful information, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report, determine the critical value, and sampling error. Explain what management can learn from the 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report.

2) Natural History magazine has published a listing of the maximum speeds, in mph, for a wide variety of animals. A random sample of four of these animals, along with their maximum speeds, is shown below: Cheetah 70 mph Domestic Cat 30 mph Giraffe 32 mph Elephant 25 mph a) Compute the sample mean maximum speed of this sample of size 4. Show units. Do not approximate. b) The true mean maximum speed for all of the animals in this study is 30 mph. (  = 30 mph) Assuming there have been no mistakes in collecting, recording, or computing, find the sampling error. Show units.

4) A magazine reported the results of a survey in which readers were asked to send their responses to several questions regarding good eating. DataSet for question 4,5,6 is the reported results to the question, How often do you eat chocolate? Based on the data answer the following questions.

a) Were the responses to this survey obtained using voluntary sampling technique? Explain

b) What type of bias may be present in the response?

c) is 13% a reasonable estimate of the proportion of all Americans who eat chocolate frequently? Explain.

5) A magazine reported the results of a survey in which readers were asked to send in their responses to several questions regarding anger. DataSet2 for Question 5 shows the reported results to the question, How long do you usually stay angry? Answer the following questions based on the data.

a) Were the responses to this survey obtained using voluntary sampling technique?

b) What type of bias may be present in the response?

c) Is 22% a reasonable estimate of the proportion of all Americans who hold a grudge indefinitely? Explain.

6) Students in marketing class have been asked to conduct a survey to determine whether or not there is demand for an insurance program at a local college. The Students decided to randomly select students from the local college and mail them a questionnare regarding the insurance program. Of the 150 questionnaire that were mailed, 50 students responded to the following survey item: Pick the Category which best describes your interest in an insurance program. DataSet2 for question 6 shows the responses. Use this data to answer the following question.

a)What type of bias may be present in the response?

b) is 50% a reasonable estimate of the proportion of all students who would be very interested in an insurance program at a local college? Explain.

c) is 50% a reasonable estimate of the proportion of all business majors who would be very interested in an insurance program at a local college? Explain.

d) What strategies do you think the marketing students could have used in order to get a less biased response to their survey?

e) Suppose the program was created and only a few people registered. How could the survey question have been reworded to better predict the actual enrollment?

DATA SET FOR QUESTION 4, 5 AND 6

Table for Question 4 – Survey Responses

Category % of Responses

Frequently 13

Occasionally 45

Seldom 37

Never 5

Table for Question 5 – Survey Responses

Category % of Responses

A few hours or less 48

A day 12

Several days 9

A month 1

I hold a grudge indefinitely 22

It depends on the situation 8

Table for Question 6 – Survey Responses
Category % of Responses
Very Interested 50
Somewhat Interested 15
Interested 10
Not Very Interested 5
Not At All Interested 20

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 12.9 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 12.9 weeks and that the population standard deviation is 4.8 weeks. Suppose you would like to select a random sample of 99 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 12 and 12.6. P(12 < X < 12.6) =

Find the probability that a sample of size n = 99 is randomly selected with a mean between 12 and 12.6. P(12 < M < 12.6) =