Question

A) 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 185 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(mean)	s
Food stores	18.75	24.77
Mass merchandisers	32.34	33.27
Pharmacies	48.35	35.50

We do not know the population standard deviations, but a sample standard deviation s from so large a sample is usually close to σ. Use s in place of the unknown σ in this exercise.

- What population do you think the authors of the study want to draw conclusions about?

the American public (this is correct)

- What population are you certain they can draw conclusions about?

citizens of Indianapolis (this is correct)

- 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	( ? , ? )

B) The one-sample t statistic for testing

H₀: μ = 10

H_a: μ > 10

from a sample of n = 23 observations has the value t = 2.17.

- What are the degrees of freedom for this statistic?
n = 22 (this is correct)

- Give the two critical values t* from the t distribution critical values table that bracket t.
  ? < t < ?

- If you have software available, find the exact P-value. (Round your answer to four decimal places.)

Answer 1

z-value for 90% CI is 1.645

CI for food stores
ME = 1.645 * 24.77/sqrt(185) = 2.9958

CI = (18.75 - 2.9958, 18.75 + 2.9958)
= (15.7542, 21.7458)

For Mass merchandisers
ME = 1.645 * 33.27/sqrt(185) = 4.0238

CI = (32.34 - 4.0238, 32.34 + 4.0238)
= (28.3162, 36.3638)

For Pharmacies
ME = 1.645 * 35.5/sqrt(185) = 4.2935

CI = (48.35 - 4.2935, 48.35 - 4.2935)
= (44.0565, 52.6435)

B)
Critical values are 2.074 < t < 2.508

p-value = 0.0205
=1 - T.DIST(2.17,22,TRUE)