Chapter 8, Problem 56PS

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 40 respondents is selected, and each respondent is instructed to keep a detailed record of time spent engaged viewing content across all screens (traditional TV, DVD/Blu-ray, game console, Internet on a computer, video on a computer, video on a mobile phone) in a particular week. The results are as follows:

$•$ Content viewing time per week: $\bar{X}=41$ hours, $S=3.5$ hours.

$•$ 30 respondents have high deï¬�nition (HD) on at least one television set.

a. Construct a $95\%$ con�dence interval estimate for the mean content viewing time per week in this area.

b. Construct a $95\%$ con�dence interval estimate for the population of residents who have HD on at least television set. Suppose that the market researcher wants to take another survey in a different location. Answer these questions:

Suppose that the market researcher wants to take another survey in a different location. Answer these questions:

c. What sample size is required to be $95\%$ con�dent of estimating the population mean content viewing time to within $\pm 2$ hours assuming that the population standard deviation is equal to 5 hours?

d. How many respondents need to be selected to be $95\%$ con�dent of being within $\pm 0.06$ of the population proportion who have HD on at least television set if no previous estimate is available?

e. Based on (c) and (d). how many respondents should the market researcher select if a single survey is being conducted?