A grocery store manager believes that the mean amount spent by customers on dairy products per visit is higher in stores in which the dairy section is in the central part of the store compared with stores that have the dairy section at the rear of the store. To consider relocating the dairy products, the manager feels that the increase in the mean amount spent by customers must be at least 25 cents. To determine whether relocation is justified, her staff selected a random sample of 25 customers at stores in which the dairy section is central in the store.

She selected a second sample of 25 customers in stores with the dairy section at the rear of the store. The following sample results were observed:

Central Dairy Rear Dairy x1 = +3.74 x2 = +3.26 s1 = +0.87 s2 = +0.79

a. Conduct a hypothesis test with a significance level of 0.05 to determine if the manager should relocate the dairy products in those stores that have their dairy products in the rear of the store. Assume equal population variances.

b. If a statistical error associated with hypothesis testing was made in this hypothesis test, what error could it have been? Explain.