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## Statistics Question

1. More on the power for a different alternative. A one-sided test of the null hypothesis μ = 20 versus the alternative μ = 35 has power equal to 0.60. Will the power for the alternative μ = 28 be higher or lower than 0.73? Explain your answer.
• Where do you buy? Consumers can purchase nonprescription medications at food stores, mass merchandise stores such as Target and Walmart, 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 201 people chosen at random from the Indianapolis telephone directory.

What population do you think the authors of the study want to draw conclusions about? What population are you certain they can draw conclusions about?

• Where do you buy? Consumers can purchase nonprescription medications at food stores, mass merchandise stores such as Target and Walmart, 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 201 people chosen at random from the Indianapolis telephone directory.

 Store type Sample Mean Sample Standard Deviation Food stores 18.67 24.95 Mass merchandisers 32.38 33.37 Pharmacies 48.60 35.62

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.

Question: Give 95% confidence intervals for the mean performance for each type of store. In the form below, type the confidence intervals using the following format:

• Food Stores (Lower Bound, Upper Bound)
• Mass Merchandisers (Lower Bound, Upper Bound)
• Pharmacies (Lower Bound, Upper bound)

[Note: For an example on formatting, if my sample mean is 5, and my margin of error is 2, then I would write the confidence interval as (3, 7). My lower bound is 3 and my upper bound is 7]

Please provide your interval bounds in decimal form to 2 decimal places.

• Based on the confidence intervals calculated in the previous question, are you convinced that consumers think that pharmacies offer higher performance than the other types of stores?

Please explain your reasoning based on the confidence interval values calculated in the previous question.

• Meaning of “statistically significant.” When asked to explain the meaning of “statistically significant at the α = 0.01 level,” a student says, “This means there is only probability 0.01 that the null hypothesis is true.” Is this an essentially correct explanation of statistical significance? Explain your answer.