Question

Question 1:
There have been many studies that suggest global climate change is affecting the population of polar bears. One measure of the health of a polar bear population is weight, and the mean weight for a male polar bear is approximately 900 pounds with population
deviation 78 pounds. A recent study suggests that the polar bears in the Chukchi Sea are
doing very well despite changes in the climate. A random sample of 14 male polar bears
from the Chukchi Sea was obtained. The sample mean weight was 1016 pounds. Assume
the underlying weight distribution of polar bears is normal.

a. Suppose we wish to perform a significance test with Ha : µ > 900, what is your decision
at the significance level of 0.01?

b. What is your decision at the significance levle of 0.05 and 0.001 respectively?

d. In part a, what is the type I error rate α?

e. In part a, if the true population mean is 1000 pounds, what is the type II error rate
β?

Answer 1

A to D has been solved.

a. Suppose we wish to perform a significance test with Ha : µ > 900, what is your decision at the significance level of 0.01

b. What is your decision at the significance levle of 0.05 and 0.001 respectively?

At the level of significance of 0.05 and 0.001, we still reject the null hypothesis since the pvalue is less than the level of significance.

d. In part a, what is the type I error rate α?

It is equal to the level of significance 0.01