A quahog is a chewy Atlantic hard-shell clam with a blue-gray shell. Quahogs have different names, depending on size; for example, the width of a littleneck clam is under 5 centimeters (across the...

A quahog is a chewy Atlantic hard-shell clam with a blue-gray shell. Quahogs have different names, depending on size; for example, the width of a littleneck clam is under 5 centimeters (across the shell). The historical mean width of a littleneck is 4.75 cm. Following a recent oil spill off the coast of Maine, a random sample of 46 littlenecks was obtained and the width of each was recorded. The summary statistics were x 5 4.66 cm and s = 0.25 cm.

a. Use a one-sided, left-tailed hypothesis test to show that there is evidence to suggest the mean width of littlenecks has decreased. Assume the population of littleneck widths is normal and use a =0.01.

b. Explain why there is statistical evidence that the population mean has decreased even though the sample mean (4.66) is so close to the historical mean (4.75).

c. Find bounds on the p value associated with this hypothesis test.