Question: The Glen Valley Steel Company manufacturers steel bars.  If the production process is working properly, it turns out steel bars with mean length of at least 2.8 feet with a standard deviation of 0.20 feet.  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?

1. If you want to test the null hypothesis at the 0.05 level of significance, what decision would you make using the critical value approach to hypothesis testing?
2. If you want to test the null hypothesis at the 0.05 level of significance, what decision would you make using the p-value approach to hypothesis testing?
3. Interpret the meaning of the p-value in this problem.
4. Compare your conclusions in (a) and (b).

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