Chapter 8, Problem 30PS

What do you value most when shopping in a retail store? According to a Time Trade survey, $26\%$ of consumers value personalized experienced most.

a. Suppose that the survey had a sample size of $n=1,000.$ Construct a $95\%$ confidence interval estimate for the population proportion of consumers that value personalized experience most when shopping in a retail store?

b. Based on (a), can you claim that more than a quarter of all consumers value personalized experience most when shopping in a retail store?

c. Repeat part (a) and (b), assuming that the survey had a sample size of $n=10,000.$

d. Discuss the effect of sample size on confidence interval estimation.