Consumers can purchase nonprescription medications at food s

Consumers can purchase nonprescription medications at food stores, mass merchandise stores such as Kmart and Wal-Mart, or pharmacies. About 45% of consumers make such purchases at pharmacies. What accounts for the popularity of pharmacies, which often charge higher prices? A study examined consumers\' perceptions of overall performance of the three types of stores, using a long questionnaire that asked about such things as \"neat and attractive store,\" \"knowledgeable staff,\" and \"assistance in choosing among various types of nonprescription medication.\" A performance score was based on 27 such questions. The subjects were 218 people chosen at random from the Indianapolis telephone directory. Here are the means and standard deviations of the performance scores for the sample.

Give 90% confidence intervals for the mean performance for each type of store.

Solution

Given a=1-0.9=0.1, Z(0.05) = 1.64 (from standard normal table)

For food stores:

So the lower bound is

xbar - Z*s =18.46 - 1.64*24.64 =-21.9496

So the upper bound is

xbar + Z*s =18.46 + 1.64*24.64 =58.8696

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For mass merchandisers:

So the lower bound is

xbar - Z*s =32.36 - 1.64*33.63 =-22.7932

So the upper bound is

xbar + Z*s =32.36 + 1.64*33.63 =87.464

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For pharmacies:

So the lower bound is

xbar - Z*s =48.83 - 1.64*35.40 =-9.226

So the upper bound is

xbar + Z*s =48.83 + 1.64*35.40 =106.886