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In: Statistics and Probability

Consumers can purchase nonprescription medications at food stores, mass merchandise stores such as Target and Wal-Mart,...

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 196people 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 24.97
Mass merchandisers 32.55 33.68
Pharmacies 48.74 35.41

(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

( , )

Solutions

Expert Solution

Since n is very large, we use the z distribution. The Zcritical (2 tail) for = 0.10 is 1.645

90% Confidence interval for the Food Stores:

Given: = 18.49, s = 24.97, n = 196

The Confidence Interval is given by ME, where

The Lower Limit = 18.49 - 2.934 = 15.556

The Upper Limit = 18.49 + 2.934 = 21.424

The 90% Confidence Interval is (15.556 , 21.424)

__________________________________________________________________________

90% Confidence interval for the Mass Merchandisers:

Given: = 32.55, s = 33.68, n = 196

The Confidence Interval is given by ME, where

The Lower Limit = 32.55 - 3.957 = 28.593

The Upper Limit = 32.55 + 3.957 = 36.507

The 90% Confidence Interval is (28.593 , 36.507)

__________________________________________________________________________

90% Confidence interval for the Pharmacies:

Given: = 48.74, s = 35.41 n = 196

The Confidence Interval is given by ME, where

The Lower Limit = 48.74 - 4.161 = 44.579

The Upper Limit = 48.74 + 4.161 = 52.901

The 90% Confidence Interval is (44.579 , 52.901)

__________________________________________________________________________

orchestra answered 2 years ago
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