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 200 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 18.49 24.52 Mass merchandisers 32.38 33.03 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? sick people consumers the American public pharmacies citizens of Indianapolis What population are you certain they can draw conclusions about? the American public pharmacies sick people citizens of Indianapolis consumers (b) Give 90% 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

Given that,

(a) What population do you think the authors of the study want to draw conclusions about? sick people consumers the American public pharmacies citizens of Indianapolis What population are you certain they can draw conclusions about? the American public pharmacies sick people citizens of Indianapolis consumers

Here n = 200

So population follows normal distribution.

b) Give 90% confidence intervals for the mean performance for each type of store. (Round your answers to three decimal places.) Food stores , Mass merchandisers , Pharmacies

We can find confidence interval in ti-83 calculator.

steps :

STAT --> TESTS --> 7:ZInterval --> ENTER --> Highlight on STats --> ENTER --> Input all the values --> Calculate --> ENTER

90% confidence intervals for the mean performance for food store is (15.638, 21.342)

90% confidence intervals for the mean performance for Mass merchandisers is (28.538, 36.222)

90% confidence intervals for the mean performance for pharmacies is (44.332, 52.528)

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

We can see that the confidence limits for Pharmacies are greator than other two.

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