Question: The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars that are normally distributed with mean length of at least 2.8 feet, with a standard deviation of 0.20 foot (as determined from engineering specifications on the production equipment involved). Longer steel bars can be used or altered, but shorter bars must be scrapped. You select a sample of 25 bars, and the mean length is 2.73 feet. Do you need to adjust the production equipment?
a. If you test the null hypothesis at the 0.05 level of significance, what decision do you make using the critical value approach to hypothesis testing?
b. If you test the null hypothesis at the 0.05 level of significance, what decision do you make using the p-value approach to hypothesis testing?
c. Interpret the meaning of the p-value in this problem.
d. Compare your conclusions in (a) and (b).