Question

A market researcher for a consumer electronics company wants to study the media viewing behavior of residents of a particular area. A random sample of 80 respondents is selected, and each respondent is instructed to keep a detailed record of time spent engaged viewing content across all screens in a particular week. The results are as follows: Content viewing time per week: X = 44 hours, S = 5.7 hours. 28 respondents have high definition (HD) on at least one television set. Complete parts (a) through (e) below. a. Construct a 90% confidence interval estimate for the mean content viewing time per week in this area. Isusa (Round to two decimal places as needed.) b. Construct a 90% confidence interval estimate for the population proportion of residents who have HD on at least one television set. Osas (Round to four decimal places as needed.) c. Suppose that the market researcher wants to take another survey in a different location. What sample size is required to be 90% confident of estimating the population mean content viewing time to within + 2 hours assuming that the population standard deviation is equal to 6 hours? (Type a whole number.) d. How many respondents need to be selected to be 90% confident of being within 10.05 of the population proportion who have HD on at least one television set if no previous estimate is available? (Type a whole number.) Enter your answer in each of the answer boxes. e. Based on (C) and (d), how many respondents should the market researcher select if a single survey is being conducted? (Type a whole number.) Enter your answer in each of the answer boxes.

Answer 1

a. Construct a 90% confidence interval estimate for the mean content viewing time per week in this area. Isusa

90% confidence interval estimate for the mean content viewing time per week: (41.75, 46.25)

b. Construct a 90% confidence interval estimate for the population proportion of residents who have HD on at least one television set. Osas

90% confidence interval estimate for the population proportion: (0.1867, 0.3833)

c. Suppose that the market researcher wants to take another survey in a different location. What sample size is required to be 90% confident of estimating the population mean content viewing time to within + 2 hours assuming that the population standard deviation is equal to 6 hours? (Type a whole number.)

Sample size required: 653

d. How many respondents need to be selected to be 90% confident of being within 10.05 of the population proportion who have HD on at least one television set if no previous estimate is available? (Type a whole number.) Enter your answer in each of the answer boxes.

Sample size required: 461

e. Based on (C) and (d), how many respondents should the market researcher select if a single survey is being conducted? (Type a whole number.) Enter your answer in each of the answer boxes.

Sample size required: 653