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 213 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

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?

(b) What population are you certain they can draw conclusions about?

(c) Give 98% confidence intervals for the mean performance for each type of store. (Round your answers to three decimal places.)

(d)Based on these confidence intervals, are you convinced that consumers think that pharmacies offer higher performance than the other types of stores?

store type x (mean) s Food Stores 18.49 25.01 Mass Merchandisers 32.22 33.49 Pharmacies 48.85 35.72

Explanation / Answer

(a)

The authors wnat to draw conclusions about the consumers who purchase nonprescription medications at food stores, mass merchandise or pharmacies.

(b)

They can draw conclusions about Consumers of nonprescription medications in Indianapolis who have their names in telephone directory.

(c)

Z value of 98% confidence interval is 2.33

98% confidence interval of Food stores = (18.49 - 25.01/sqrt(213) , 18.49 + 25.01/sqrt(213))

= (16.776, 20.204)

98% confidence interval of Mass Merchandisers = (32.22 - 33.49/sqrt(213) , 32.22 + 33.49/sqrt(213))

= (29.925, 34.515)

98% confidence interval of Pharmacies = (48.85 - 35.72/sqrt(213) , 48.85 + 35.72/sqrt(213))

= (46.403, 51.297)

(d)

As, the 98% confidence intervals of each store type do not overlap, the performance scores of each store is significantly different, and since the mean performance score of pharmacies is highest among the store types, we are convinced that consumers think that pharmacies offer higher performance than the other types of stores.

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