2. A marketing company research firm is interested in estimating the difference in the proportion of households in City A who purchase groceries on-line and the proportion of households in City B who purchase groceries on-line. The company randomly samples 150 households from City A and finds 52 who purchase groceries on-line. The company also samples 135 households from City B and finds 60 who purchase groceries on-line.

a) Calculate the 90% confidence interval for the difference in rates. Interpret your results (in terms of the problem).

b) An executive who reads the results of the research claims the results are not valid since the sample sizes were not the same. Comment on that claim.