Question: A steel producer manufactures steel bars. The bars are supposed to average 2.8 feet in length. Longer bars can be shortened, but shorter bars must be scrapped. Past records indicate a standard deviation of 0.2 feet. A sample of 30 steel bars is selected.

A. State the null and alternative hypotheses to determine whether steel bars are meeting specifications, to minimize scrapping. (hint: you don’t want the bars to be too short)

B. For ? = .05, state the decision rule for rejecting the above Ho.

C. The sample of 30 bars has an average length of 2.75 feet, what conclusion can you make about the steel bars?

D. What kind of mistake could you be making by drawing the above conclusion?

E. What is the p-value associated with the average of 2.75 feet?

F. How would your answer to “C” change if the sample size was only 24 and the population standard deviation unknown?