A market researcher for a consumer electronics company wants

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 respondentent 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 (with line over top) = 15.3 hours, S = 3.8 hours.

- 27 respondents watch the evening news on a least three week nights.

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 week nights per week.

Solution

(a) Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

So 95% confidence interval is

xbar +/- Z*s/vn

--> 15.3 +/- 1.96*3.8/sqrt(40)

--> (14.12237, 16.47763)

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(b) p= 27/40 = 0.675

So 95% confidence interval is

p +/- Z*sqrt(p*(1-p)/n)

--> 0.675 +/- 1.96*sqrt(0.675*(1-0.675)/40)

--> (0.5298491, 0.8201509)