Consumers can purchase nonprescription medications at food stores, mass merchand

Question

Consumers can purchase nonprescription medications at food stores, mass merchandise stores such as Target 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. Store type x s Food stores 18.63 24.59 Mass merchandisers 32.64 33.09 Pharmacies 48.43 35.23 We do not know the population standard deviations, but a sample standard deviation s from so large a sample is usually close to . Use s in place of the unknown in this exercise. (a) What population do you think the authors of the study want to draw conclusions about? pharmacies the American public sick people citizens of Indianapolis consumers What population are you certain they can draw conclusions about? sick people citizens of Indianapolis pharmacies consumers the American public (b) Give 95% confidence intervals for the mean performance for each type of store. (Round your answers to three decimal places.) Food stores , Mass merchandisers , Pharmacies , (c) Based on these confidence intervals, are you convinced that consumers think that pharmacies offer higher performance than the other types of stores? (In Chapter 12, we will study a statistical method for comparing means of several groups.) Yes, the pharmacy interval is well above the others. Yes, the mass merchandiser interval is well above the others. Yes, the food store interval is well below the others. No, there is no clear evidence of a significant difference.

Explanation / Answer

(a) What population do you think the authors of the study want to draw conclusions about?

Answer : Sick People

What population are you certain they can draw conclusions about?

Answer: citizens of Indianapolis

(b) 95% confidence intervals

For Food stores :

95% CI = x +- Z95% (s/ sqrt(n)

all values are given above

95% CI = 18.63 +-1.96 * (24.59 / 218)

= (15.346, 21.894)

For Mass Merchandisers:

95% CI = x +- Z95% (s/ sqrt(n)

all values are given above

95% CI = 32.64 +-1.96 * (33.09 / 218)

= (28.247, 37.033)

For Pharmecies :

95% CI = x +- Z95% (s/ sqrt(n)

all values are given above

95% CI = 48.43 +-1.96 * (35.23 / 218)

= (43.753, 53.107)

As we can see that no confidence interval conicide with another confidence interval. Yes, the pharmacy interval is well above the others.

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