A manufacturer of precision measuring instruments claims that the standard deviation in the use of the instrument is at most 0.00003 mm. An analyst who is unaware of the claim, uses the instrument 8 times and obtain a sample standard deviation of 0.00001 mm.
a) Step on how to confirm using a test procedure and (alpha) level of 0.01 that there is insufficient evidence to support the claim that the standard deviation is at most 0.00003. State any necessary assumption about the underlying distribution of data.
b) Explain whythe standard deviation, s = 0.00001 is less than 0.00003, yet the statistical test procedure results do not support the claim.