A computer supplies retailer wishes to open a store in one of two Pittsburgh suburbs, Monroevilleand Greentree. To decide where to locate its store, the retailer conducts an e-mail survey of randomly selected households in each suburb, in order to measure the average yearly expenditure per household on computer supplies. 13 households from Monroeville responded to the survey: these households spent an average of $81, with a standard deviation of $20. 12 households from Greentree responded to the survey: these households spent an average of $74, with a standard deviation of $22.
a) Let 1 and 2 represent the mean expenditures per household in Monroeville and Greentree respectively. Compute the 99% confidence interval for 1 - 2.
b) Is the sample evidence sufficient to conclude which suburb spends more? To answer this question,perform a two-sided hypothesis test at = .05. State the alternative and null hypotheses, computethe observed significance level (p-value), and state the conclusion of your test. (For parts a andb, you should assume that both populations are approximately normally distributed, with equalvariances.)
In a much larger, follow-up survey, 563 households from Monroeville and 587 households from Greentree were polled. The Monroeville households spent an average of $76, with a standard deviation of $19, and the Greentree households spent an average of $80, with a standard deviationof $22.
c) Let µ1 and µ2 represent the mean expenditures per household in Monroeville and Greentree respectively. Using the sample evidence from the follow-up survey, compute the 99% confidence interval for µ1 - µ2.
d) Is the sample evidence from the follow-up survey sufficient to conclude which suburb spends more? To answer this question, perform a hypothesis test at α = .05. State the alternative and nullhypotheses, compute the observed significance level (p-value), and state the conclusion of your test.