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 209people chosen at random from the Indianapolis telephone directory. Here are the means and standard deviations of the performance scores for the sample.

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?

pharmaciessick people    the American publicconsumerscitizens of Indianapolis

What population are you certain they can draw conclusions about?

pharmaciescitizens of Indianapolis    sick peoplethe American publicconsumers

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

(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.

Store type x s Food stores 18.57 24.51 Mass merchandisers 32.28 33.01 Pharmacies 48.6 35.62

Explanation / Answer

Answer to part a)

the author is interested in the population "The American Consumers"

The population covered is "The Citizens of Indianapolis"

.

Answer to part b)

The formula of confidence interval is :

x bar - z*s /sqrt(n) , x bar + z* s/ sqrt(n)

We got n = 209

and Z critical for 98% confidence level is : 2.33

.

For Food stores: x bar = 18.57 , s = 24.51

on plugging the values we get

18.57 -2.33 * 24.51/sqrt(209) , 18.57 + 2.33*24.51/sqrt(209)

14.6197 , 22.5203

.

For Mass Merchandisers , x bar = 32.28 , s = 33.01

32.28 -2.33*33.01/sqrt(209) , 32.28 +2.33*33.01/sqrt(209)

26.9598 , 37.6002

.

For pharmacies , x bar = 48.6 , s = 35.62

48.6 - 2.33*35.62/sqrt(209) , 48.6+2.33*35.62/sqrt(209)

42.8591 , 54.3409

.

Part c)

Yes, based on the above confidence intervals , we get to know that the lower limit of pharmacies confidence interval , is higher that the upper limit of th confidence interval of food supplies and mass merchandisers. This tells us that the pharmacies have a higher performance that the other type of stores

Hence the correct answer is: Yes, the pharmacy interval is weel above the others

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