Chapter 6.2, Problem 11Q

As input for a new inflation model, economists predicted that the average cost of a hypothetical “food basket” in east Tennessee in July would be $145.75. The standard deviation $\left(\sigma \right)$ of basket prices was assumed to be $9.50, a figure that has held fairly constant over the years. To check their prediction, a sample of twenty-five baskets representing different parts of the region were checked in late July, and the average cost was $149.75. Let $\alpha =0.05$. Is the difference between the economists’ prediction and the sample mean statistically significant?