A manufacturer of precision measuring instruments claims that the standard deviation in the use of the instruments is at most 0.00002 millimeter. An analyst, who is unaware of the claim, uses the instrument eight times and obtains a sample standard deviation of 0.00001 millimeter.
(a) Confirm using a test procedure and an a level of 0.01 that there is insufficient evidence to support the claim that the standard deviation of the instruments is at most 0.00002. State any necessary assumptions about the underlying distribution of the data.
(b) Explain why the sample standard deviation, s = 0.00001, is less than 0.00002, yet the statistical test procedure results do not support the claim.