The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study used samples of sales across the USA from two different months to estimate average wheat prices. Below are the summary statistics, in dollars per bushel, for these two months. Can we claim a difference between the mean prices in the two months?

a. Construct a suitable 95% confidence interval to determine if there is a difference between the mean prices in the two months. Give your full solutions. [4 marks]

b. With 95% confidence, can we claim a difference between the mean prices in the two months? Explain why. [1 mark]

c. Test at 5% if there is a difference between the mean prices in the two months. [9 marks]

d. Are the conclusions from the confidence interval and the significance test the same? Explain why or why not. [1 mark]