A brand name that consumers recognize is a highly valued commodity in any industry. To assess brand familiarity in the furniture industry, NPD (a market research firm) surveyed 1,333 women who head U.S. households that have incomes of $25,000 or more. The sample was drawn from a database of 25,000 households that match the criteria listed above. Of the 10 furniture brands evaluated, La-Z-Boy was the most recognized brand; 70.8% of the respondents indicated they were "very familiar" with La-Z-Boy.
a. Describe the population being investigated by NPD.
b. In constructing a confidence interval to estimate the proportion of households that are very familiar with the La-Z-Boy brand, is it necessary to use the finite population correction factor? Explain.
c. What estimate of the standard error of p̂ should be used in constructing the confidence interval of part b?
d. Construct a 90% confidence interval for the true proportion and interpret it in the context of the problem.