A market researcher for a consumer electronics company wants to study the television viewing habits 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 all television viewing in a particular week. The results are as follows:
• Viewing time per week: X = 15.3 hours, S = 3.8 hours.
• 27 respondents watch the evening news on at least three weeknights.
a. Construct a 95% confidence interval estimate for the mean amount of television watched per week in this area.
b. Construct a 95% confidence interval estimate for the population proportion who watch the evening news on at least three weeknights per week.
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% confident of estimating the population mean viewing time to within ±2 hours assuming that the population standard deviation is equal to five hours?
d. How many respondents need to be selected to be 95% confident of being within ±0.035 of the population proportion who watch the evening news on at least three weeknights 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?