Question 3 [8 marks] The U.S. Army Corps of Engineers is dredging the ship channel into Port Corpus Christi to accommodate tankers and bulk carriers. The plans call for the channel to be 530 ft wide. Following completion, a random sample of 18 locations along the channel was selected, and the width at each location was measured. The sample mean was =523.72. Assume the distribution of channel widths is normal and =12.4.

a. [6 marks] Is there any evidence to suggest the mean width of the channel is less than 530 ft? Use =0.05.

b. [2 marks] Find the p value associated with this hypothesis test.