Lake Vostok is Antarctica’s largest and deepest subsurface lake. It is buried under approximately 2 miles of ice, and scientists believe it contains evidence of thousands of tiny organisms and fish....

Lake Vostok is Antarctica’s largest and deepest subsurface lake. It is buried under approximately 2 miles of ice, and scientists believe it contains evidence of thousands of tiny organisms and fish. The mean depth of the lake is believed to be 344 meters. A random sample of the depth of this lake was obtained. Assume the underlying distribution is normal and that s = 30 meters.

a. Conduct a hypothesis test to determine whether there is any evidence to suggest the mean depth is less than 344 meters. Use a = 0.01.

b. Find the probability of a type II error if the true mean depth of the lake is 315 meters; that is, find b(315).

c. Carefully sketch a graph illustrating the probability found in part (b) using density curves for X .

d. Find b(310).