Steel Company

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. 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 and the sample standard deviation is 0.20 foot. 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).   

Question

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of  the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a  particular sample the mean amount dispensed is 8.159 ounce and the standard   deviation of 0.051 ounce.   

 a) Is there evidence that the population mean amount is different from 8.17 ounce? (Use a 0.05 level of significance).   

b) Determine the p-value and interpret   its meaning.