A grocery store franchise is planning to open a new store in a large southern town. The company is concerned about how much money their customers spend per week on food. The company surveyed 45 customers and asked them how much they spend per week on food. The average purchase for the sample was $232, and a sample standard deviation was $60.

(a) Construct a 99% confidence interval for the average purchase.

(b) Interpret the confidence interval in non-mathematical terms.

The company decides that if the average purchase falls below $250, then they will have to reduce costs by offering fewer organic foods.

(c) State the hypotheses.

(d) Calculate the appropriate test statistic for this test. Calculate the p-value for the test statistic.

(e) Sketch the distribution of the test statistic assuming the null is true, mark the test statistics, and shade the area that corresponds to the p-value.

(f) Make the appropriate inference from the test. Use=0.05.