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A lathe is set to cut bars of steel into lengths of 9 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 9 centimeters. A sample of 100 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 9.085 centimeters.
Suppose the population standard deviation is 0.335 centimeters.
a. Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment. Please write out all steps used.
b. Compute the test statistic. Please write out all steps used.
c. Using the p-value approach, what is your conclusion? Let α= 0.05. Please write out all steps used.
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