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Chapter 1: Problem 77

To examine whether playing music in a store increases the amount customers spend, we randomly assign some stores to play music and some to stay silent and compare the average amount spent by customers.

Short Answer

Expert verified
After conducting the necessary statistical analysis, a decision should be made based on the result of the t-test (p-value) and the significance level. This decision will either reject or fail to reject the null hypothesis, providing evidence whether or not playing music in a store increases the average customer spending.

Step by step solution

01

Define the Hypothesis

The first step is to define the null and alternative hypothesis. The null hypothesis \(H_0\) is that the average spending is the same in both stores with music and without music, while the alternative hypothesis \(H_a\) is that stores that play music have a higher average customer spending than the ones that remain silent.
02

Collect and Analyze the Data

Data should be collected from the stores, keeping track of the averages of the customers' spending. Next, perform a statistical test (t-test for two independent samples) to compare the means of the two groups (stores that play music and stores that do not play music). This requires calculation of the mean and standard deviation for both groups, as well as the sample size of each group.
03

Formulate the Decision Rule

A decision rule must be set, often depending on the chosen significance level, usually 0.05. If the p-value from the t-test is less than the significance level, then the null hypothesis is rejected, in favor of the alternative hypothesis.
04

Make a Decision and Interpret the Result

After the t-test is done, compare the resulting p-value with the significance level. If the p-value is below the significance level, the decision is to reject the null hypothesis. Meaning, there is strong evidence that stores that play music have a higher average spending compared to stores that remain silent. If the p-value is above the significance level, the decision is to fail to reject the null hypothesis, implying that there is not enough evidence to support the claim that playing music in the store increases the average customer spending.

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