Question: Question 1: The diameter of aluminum alloy rods produced on an extrusion machine is known to have a variance of 0.09 inch². The quality engineer suspects that the mean rod diameter is less than 5.0 inch, and he collects a random sample of 36 rods which has an average diameter of 4.8 inch.

(a) Test the hypothesis that the mean rod diameter is less than 5.0 inch at significance level of 0.05. (8 points)

(b) Find the p-value for this hypothesis test. (6 points)

(c) Construct a 95% confidence interval corresponding to the hypothesis test and determine whether this interval supports or rejects the engineer’s suspect. (6 points)