Question

A situation is described for a statistical test. In each case, define the relevant parameter(s) and state the null and alternative hypotheses. Testing to see if average sales are higher in stores where customers are approached by salespeople than in stores where they aren't.

Short answer

The parameter is average sales. The null hypothesis is \(H_0: \mu_1 - \mu_2 = 0\), and the alternative hypothesis is \(H_A: \mu_1 - \mu_2 > 0\).

Step-by-step solution

Identify the Parameter

The parameter that will be compared in this study is the average sales. We will denote the average sales where customers are approached by salespeople as \(\mu_1\) and where they aren't approached as \(\mu_2\).

State the Null Hypothesis

The null hypothesis suggests that there is no difference between the parameters. So we state it as \(H_0: \mu_1 - \mu_2 = 0\), meaning the average sales are the same whether or not customers are approached by salespeople.

State the Alternative Hypothesis

The alternative hypothesis represents the scenario we are interested in proving, i.e., the average sales are higher in stores where customers are approached by salespeople than in stores where they aren't. Thus we phrase it as \(H_A: \mu_1 - \mu_2 > 0\).