Question

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

To find out if playing music influences customer spending, define hypotheses (\(H_0\), \(H_1\)), conduct an experiment, collect data, perform a statistical test (such as a t-test), and interpret the results. The conclusion would be based on the p-value obtained.

Step-by-step solution

Define the Null and Alternative Hypothesis

The null hypothesis (\(H_0\)) is that there's no difference on average in the amounts spent by customers, regardless of whether music is played or not. The alternative hypothesis (\(H_1\)) is that there is a difference in the amounts spent by customers, depending on whether music is played.

Conduct the Experiment and Collect Data

The experiment can be conducted by randomly assigning the stores to play music or remain silent, then collecting data about the average spend of customers in those stores.

Perform a Statistical Test

Apply an appropriate statistical test, such as a t-test, to compare the average amounts spent by customers in the two groups of stores. Calculate the test statistic and the p-value.

Interpret the Results

If the p-value is less than or equal to 0.05, reject the null hypothesis. This means there's a statistically significant difference in amounts spent by customers and music has an effect. If it's above 0.05, fail to reject the null hypothesis, implying that the music doesn't necessarily influence spending.