Question

The engineers at the lab have completed a pilot run of a new design of a light fixture to be produced on an injection molding press. Their analysis of the part shrinkage data associated with the new design shows an average of 1.3% and a standard deviation of 0.33%. Accordingly, they have concluded that the new fixture satisfies very well the tolerance specification, which states that no fixture should shrink more than 2.5%. In fact, they have also estimated the rejection rate for the new process at about 150 per million. You are requested to TEST the engineers' analyses and conclusions. The test data used by the engineers is shown in the table below:

1.18 1.20 0.96 1.73 1.17 1.33 1.19 0.86 1.22 1.05 1.36 2.11 1.45 1.03 0.97 1.11 1.31 1.87 1.49 1.12 1.09 1.62 0.99 1.32 1.00 0.87 2.43 1.47 1.18 1.30 0.93 1.44 1.06 1.28 1.61 1.08 1.15 1.26 1.78 1.33 1.26 0.95 1.82 1.30

Suggest a method of analysis if you find that you do not agree with the assumptions, the method of analysis, and/or the results.

Answer 1

H0: Population mean is less than or equal to 2.5%
H1: Population mean exceeds 2.5%

Sample mean = 1.30
Sample std. dev. = 0.33

The test statistic is given by (we chose standard normal distribution as we have a sample size more than 30) -

i.e. Z = -24.12 which is less than the critical value 1.64 for a one-sided test of 95% confidence level. So, H0 cannot be rejected and it is taken that the population mean is less than or equal to 2.5% at a 95% confidence level.

Note that one of the essential assumptions of the one-sample Z-test is that the population should be normally distributed. But as we can see above, the Anderson Darling test for normality fails at 05% level as the p-value is less than 0.05. So, the samples are perhaps taken in a non-random manner which is not congruent with the hypothesis test.