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 consumersâ€™ perceptions of overall performance of the three types of store using a long questionnaire that asked about such things as â€œneat and attractive store,â€ â€œknowledgeable staff,â€ and â€œassistance in choosing among various types of nonprescription medication.â€ 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 Â Store type$1rn $1rn $1rn $1rn$1rn x$1rn $1rn $1rn Â Â s
$1rn Â Food stores$1rn $1rn $1rn Â Â Â 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 Â Â Â 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 Ïƒ. Use s in place of the unknown Ïƒ 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.