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 millimeter.

(a) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeter? Use α = 0.01. State any necessary assumptions about the underlying distribution of the data. Find the P-value for this test.

(b) Suppose that the actual standard deviation of hole diameter exceeds the hypothesized value by 50%. What is the probability that this difference will be detected by the test described in part (a)?

(c) If σ is really as large as 0.0125 millimeters, what sample size will be required to detect this with power of at least 0.8?