# Statistics Question

Complete the following problems:

Problems 9.71, 9.72, 9.73

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Problems 10.60, 10.63, 10.66

• Problem 9.71::::: IAB conducted a study of 821 U.S. adults to understand the behavioral shift of consumers’ TV viewing experience. The study found that 460 of U.S. adults own streaming enabled TVs, including smart TVs and video streaming devices.
• Source: The Changing TV Experience: 2017, available at bit.ly/2sz4Mal.
• The authors of the report imply that the survey proves that more than half of all U.S. adults own streaming enabled TVs, including smart TVs and video streaming devices.

Use the six-step p-value approach to hypothesis testing and a 0.05 level of significance to try to prove that more than half of all U.S. adults own streaming enabled TVs, including smart TVs and video streaming devices.

Based on your result in (a), is the claim implied by the authors valid?

Suppose the study found that 428 of U.S. adults own streaming enabled TVs, including smart TVs and video streaming devices. Repeat parts (a) and (b).

Compare the results of (b) and (c).

Problem 9.72::::: The owner of a specialty coffee shop wants to study coffee purchasing habits of customers at her shop. She selects a random sample of 60 customers during a certain week, with the following results:

The amount spent was

X¯=\$7.25, S=\$1.75.

Thirty-one customers say they “definitely will” recommend the specialty coffee shop to family and friends.

At the 0.05 level of significance, is there evidence that the population mean amount spent was different from \$6.50?

Determine the p-value in (a).

At the 0.05 level of significance, is there evidence that more than 50% of all the customers say they “definitely will” recommend the specialty coffee shop to family and friends?

What is your answer to (a) if the sample mean equals \$6.25?

What is your answer to (c) if 39 customers say they “definitely will” recommend the specialty coffee shop to family and friends?

Problem 9.73::::: An auditor for a government agency was assigned the task of evaluating reimbursement for office visits to physicians paid by Medicare. The audit was conducted on a sample of 75 reimbursements, with the following results:

In 17 of the office visits, there was an incorrect amount of reimbursement.

The amount of reimbursement was

X¯=\$93.70, S=\$34.55.

At the 0.05 level of significance, is there evidence that the population mean reimbursement was less than \$100?

At the 0.05 level of significance, is there evidence that the proportion of incorrect reimbursements in the population was greater than 0.10?

Discuss the underlying assumptions of the test used in (a).

What is your answer to (a) if the sample mean equals \$90?

What is your answer to (b) if 15 office visits had incorrect reimbursements?

Problem 10.60::::: Do males and females differ in the amount of time they spend online and the amount of time they spend playing games while online? A study reported that women spent a mean of 1,254 minutes per week online as compared to 1,344 minutes per week for men. Suppose that the sample sizes were 100 each for women and men and that the standard deviation for women was 60 minutes per week as compared to 70 minutes per week for men.

Source: Data extracted from Ofcom, Adults’ Media Use and Attitudes, Report 2016, bit.ly/2emgWRk.

Using a 0.01 level of significance, is there evidence of a difference in the variances of the amount of time spent online between women and men?

To test for a difference in the mean online time of women and men, is it most appropriate to use the pooled-variance t test or the separate-variance t test? Using a 0.01 level of significance, use the most appropriate test to determine if there is a difference in the mean amount of time spent online between women and men.

The report found that women spent a mean of 294 minutes per week playing games while online compared to a mean of 360 minutes per week for men. Suppose that the standard deviation for women was 15 minutes per week compared to 20 minutes per week for men.

Using a 0.01 level of significance, is there evidence of a difference in the variances of the amount of time spent playing games while online per week by women and men?

Based on the results of (c), use the most appropriate test to determine, at the 0.01 level of significance, whether there is evidence of a difference in the mean amount of time spent playing games online per week by women and men.

Problem 10.63::::: Do social shoppers differ from other online consumers with respect to spending behavior? A study of browser-based shopping sessions reported that social shoppers, consumers who click away from social networks to retail sites or share an item on a social network, spent a mean of \$126.12 on a retail site in a 30-day period compared to other online shoppers who spent a mean of \$115.55.

Source: Data extracted from “Social shoppers spend 8% more than other online consumers,” bit.ly/1FyyXP5.

Suppose that the study consisted of 500 social shoppers and 500 other online shoppers and the standard deviation of the order value was \$40 for social shoppers and \$10 for other online shoppers. Assume a level of significance of 0.05.

Is there evidence of a difference in the variances of the order values between social shoppers and other online shoppers?

Is there evidence of a difference in the mean order value between social shoppers and other online shoppers?

Construct a 95% confidence interval estimate for the difference in mean order value between social shoppers and other online shoppers.

Problem 10.66::::: The owner of a restaurant that serves Continental-style entrées has the business objective of learning more about the patterns of patron demand during the Friday-to-Sunday weekend time period. She decided to study the demand for dessert during this time period. In addition to studying whether a dessert was ordered, she will study the gender of the individual and whether a beef entrée was ordered. Data were collected from 630 customers and organized in the following contingency tables:

GENDER

DESSERT ORDERED Male Female Total

Yes ?96 ?50 146

No 234 250 484

Total 330 300 630

BEEF ENTRÉE

DESSERT ORDERED Yes No Total

Yes ?74 ?68 142

No 123 365 488

Total 197 433 630

At the 0.05 level of significance, is there evidence of a difference between males and females in the proportion who order dessert?

At the 0.05 level of significance, is there evidence of a difference in the proportion who order dessert based on whether a beef entrée has been ordered?

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