The modulus of rupture (MOR) for a particular grade of pencil lead is known to have a standard deviation of 250 psi. Process standards call for a target value of 6500 psi for the true mean MOR. For each batch, an inspector tests a random sample of 16 leads. Management wishes to detect any change in the true mean MOR. (Assume normal distribution.)

a. A recent random sample yielded a sample mean of 6490. Conduct a hypothesis test to determine whether the true mean MOR has changed from the target. Use a 0.10 significance level.

b. Find the p-value associated with the test in part a. c. In Exercise 4.4, you constructed a 90% confidence interval for this situation. Use this interval to determine whether the true meanMOR has changed. Discuss the relationship of the 90% confidence interval and the corresponding hypothesis test.

d. Find the power of this test to detect a change in the true mean MOR to 6400. e. Find the sample size required to achieve an approximate power of 0.85 when the true mean MOR is 6400. f. What did you assume to do these analyses? How can you check these assumptions?