Consumers can purchase nonprescription medications at food stores, mass merchandise stores such as Kmart and Walmart, or pharmacies. About 45% of consumers make such purchases at pharmacies. What accounts for the popularity of pharmacies, which often charge higher prices? Astudy examined consumers’ perceptions of overall performance of the three types of store 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 201 people chosen at random from the Indianapolis telephone directory. Here are the means and standard deviations of the performance scores for the sample:18

$1rn  Store type$1rn $1rn $1rn $1rn$1rn x$1rn $1rn $1rn   s

$1rn  Food stores$1rn $1rn $1rn    18.67$1rn$1rn 24.95

Mass merchandisers$1rn$1rn 32.38$1rn$1rn 33.37

Pharmacies$1rn $1rn $1rn $1rn$1rn 48.60$1rn    35.62

We do not know the population standard deviations, but a sample standard deviation s from so large a sample is usually close to σ. Use s in place of the unknown σ in this exercise.

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

can draw conclusions about?

(b) Give 95% confidence intervals for the mean performance for each type of store.

(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 the means of several groups.


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