8.5 A market researcher selects a simple random sample ofn=100n=100Twitter users from a population of more than 100 million Twitter-registered users. After analyzing the sample, she states that she has 95% confidence that the mean time spent on Twitter per day is between 15 and 57 minutes. Explain the meaning of this statement.

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.

City	Weekly Commuting Time
Austin	132
Baltimore	153
Boston	160
Charlotte	132
Chicago	161
Columbus OH	118
Dallas	140
Denver	137
Detroit	126
El Paso	117
Miami	153
Houston	148
Indianapolis	124
Jacksonville	132
Las Vegas	122
Los Angeles	152
Louisville	119
Memphis	120
Milwaukee	116
Nashville	135
New York	186
Philadelphia	158
Phoenix	130
Portland OR	131
San Antonio	129
San Diego	127
San Francisco	151
San Jose	137
Seattle	147
Washington DC	172

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:

Company	Rating	Time of Ad	First Half
NFL	7.69	Halftime	No
Amazon Alexa	7.34	Fourth Quarter	No
Microspft	7.07	Fourth Quarter	No
Hyundai	7.05	Fourth Quarter	No
Verizon	6.95	Third Quarter	No
M & Ms	6.51	First Quarter	Yes
Bubly	6.43	Third Quarter	No
Budweiser	6.41	Fourth Quarter	No
Google	6.39	Second Quarter	Yes
Audi	6.38	Second Quarter	Yes
Google	6.37	Third Quarter	No
Mercedes-Benz	6.31	Second Quarter	Yes
The Washington Post	6.30	Second Quarter	Yes
Stella Artois	6.32	Second Quarter	Yes
Verizon	6.18	Fourth Quarter	No
Bud Light	6.14	Second Quarter	Yes
Bud Light	6.14	First Quarter	Yes
Netflix	6.11	Third Quarter	No
Planters	5.98	Second Quarter	Yes
Toyota	5.88	Second Quarter	Yes
Pepsi	5.84	First Quarter	Yes
Kia	5.84	Third Quarter	No
Bumble	5.80	First Quarter	No
T-Mobile	5.64	Fourth Quarter	No
Doritos	5.63	First Quarter	Yes
T-Mobile	5.59	Third Quarter	No
Pringles	5.25	Second Quarter	Yes
Toyota	5.52	Halftime	No
WeatherTech	5.50	First Quarter	Yes
Olay	5.34	First Quarter	Yes
Marvel Studios	5.34	First Quarter	Yes
Marvel Studios	5.34	First Quarter	Yes
Skechers	5.29	Third Quarter	No
Avocado from Mexico	5.29	Second Quarter	Yes
Universal	5.15	Second Quarter	Yes
Michelob Ultra	5.14	Third Quarter	No
Bud Light	5.11	Fourth Quarter	No
T-Mobile	5.10	Second Quarter	Yes
SimpliSafe	5.07	First Quarter	Yes
Colgate Total	5.04	Third Quarter	No
Amazon Prime Video	4.96	Third Quarter	No
Expensify	4.95	Second Quarter	Yes
Bud Light	4.96	Third Quarter	No
Hulu	4.85	First Quarter	Yes
Devour	4.84	Third Quarter	No
T-Mobile	4.81	First Quarter	Yes
Ron & Viv Spiked Seltzer	4.63	First Quarter	Yes
Norwegian Cruise Lines	4.61	First Quarter	Yes
ADT	4.59	Halftime	No
WeatherTech	4.55	Fourth Quarter	No
MIchelob Ultra Pure Gold	4.50	Fourth Quarter	No
Sprint	4.45	Second Quarter	Yes
Mint Mobile	4.45	Second Quarter	Yes
Peposi Proclean	4.38	Second Quarter	Yes
Turkish Airlines	4.32	Second Quarter	Yes
TurboTax	4.22	Second Quarter	Yes
Wix.com	3.97	Third Quarter	No
Burger King	3.63	Fourth Quarter	No

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.

8.43An 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?