Many scientists are concerned about changes in the ice thickness due to global warming. Suppose the historical mean thickness of the ice just off the coast of Barrow, Alaska, is 3.32 meters. A random sample (????=28

n=28) of the ice thickness near Barrow during 2008 was obtained. Assume????=2.8

=2.8meters, and the underline distribution is normal.

1(5 points). Suppose the sample mean ice thickness is 4.036 meters, conduct a hypothesis test to determine whether there is any change in the mean ice thickness. Use????=0.01

=0.01.

2(5 points). Find the probability of a type II error if the true ice mean thickness is 3.0. That is????(3.0).