(1.5 points) If the standard deviation of hole diameter exceeds 0.01 millimeters, there is an unacceptably high probability that the rivet will not fit. Suppose that n = 15 and s = 0.008 millimeters.
a. Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters? Use a = 0.01. State your conclusions explicitly. What does rejecting or not rejecting null hypothesis mean?
b. Find the P-value for this test.
c. Suppose that the actual standard deviation of hole diameter exceeds the hypothesized value by 50%. What is the beta in part (a)? Show ?.
d. If s is really as large as 0.0125 millimeters, what sample size will be required to defect this with power of at least 0.8? Show ?.