A marketing research firm is interested in determining whether there is a difference between the proportion of households in Chicago and the proportion of households in Milwaukee who purchase groceries online. The research firm decided to randomly sample households earning more than $50,000 a year in the two cities and ask them if they purchased any groceries online last year. The random sample involved 150 Chicago households and 135 Milwaukee households. The results of the sample can be found in the file Online Groceries.
a. Construct a 95% confidence interval estimate for the difference between the two population proportions.
b. At the 0.10 level of significance, can the marketing research firm conclude that a greater proportion of households in Chicago earning more than $50,000 annually buys more groceries online than do similar households in Milwaukee? Support your answer with the appropriate hypothesis test.