8.7Consider the confidence interval estimate discussed inProblem8.5. Suppose the population mean time spent on Twitter is 46 minutes a day. Is the confidence interval estimate stated inProblem8.5correct? Explain.

8.19How much time do commuters living in or near cities spend commuting to work each week? The file [Commuting Time] contains the average weekly commuting time in 30 U.S. cities.

Source:Data extracted from Office of the New York City Comptroller, "NYC Economics Brief," March 2015, p. 3.

1. a.Construct a 95% confidence interval estimate for the population mean commuting time.
2. b.Interpret the interval constructed in (a).
3. c.What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?
4. d.Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

8.20The Super Bowl, watched by close to 200 million Americans, is also a big event for advertisers. The file [Super Bowl Ad Ratings] contains the rating of ads that ran between the opening kickoff and the final whistle.

Source:Data extracted fromwww.admeter.usatoday.com/results/2019

For ads that ran before halftime and ads that ran at halftime or after separately:

a.Construct a 95% confidence interval estimate for the population mean ad rating.

b.Interpret the interval constructed in (a).

c.What conclusions can you reach about the ad ratings of ads that ran before halftime and ads that ran at halftime or after?

d.What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?

e.Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

8.28 A cellphone provider has the business objective of wanting to estimate the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results indicate that 135 of the subscribers would upgrade to a new cellphone at a reduced cost.

1. a.Construct a 99% confidence interval estimate for the population proportion of subscribers that would upgrade to a new cellphone at a reduced cost.
2. b.How would the manager in charge of promotional programs use the results in (a)?

8.43An advertising media analyst wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 45 minutes.

1. a.What sample size is needed if the media analyst wants to be 90% confident of being correct to within55minutes?
2. b.If 99% confidence is desired, how many consumers need to be selected?

8.48 Cybersecurity is a critical business issue that demands the attention of business and IT executives. According to a study released by PwC, 38% of surveyed business and IT executives reported phishing scams at their institutions.

Source: Data extracted from "Toward new possibilities in threat management," PwC, 2017 pwc.to/2kwhPJv.

a. If you conduct a follow-up study to estimate the population proportion of business and IT executives reporting phishing scams at their institutions, would you use a of 0.38 or 0.50 in the sample size formula?

b. Using your answer in part (a), find the sample size necessary to estimate, with 95% confidence, the population proportion to within 0.03.