A manufacturing process produces ball bearings with diameters having a normal distribution and a standard deviation of σ = 0.04 cm. Ball bearings that have diameters that are too small or too large are undesirable. To test the null hypothesis that µ _ 0.50 cm, a sample of 25 is randomly selected and the sample mean is found to be 0.51.
a. Design null and alternative hypotheses such that rejection of the null hypothesis will imply that the ball bearings are undesirable.
b. Using the decision rule established in part a, what is the p-value for the sample results?
c. If the decision rule in part a is used with a = 0.02 what is the critical value for the test statistic?