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.
a. A recent random sample yielded a sample mean of 6490 psi. Conduct an hypothesis test to determine whether the true mean MOR has changed from the target. Use a 0.10 significance level.
b. Construct a 90% confidence interval for this situation. Use this interval to determine whether the true mean MOR has changed. Discuss the relationship of the 90% confidence interval and the corresponding hypothesis test.
c. Find the power of this test to detect a change in the true mean MOR to 6400 psi.
d. Find the sample size required to achieve an approximate power of 0.85 when the true mean MOR is 6400 psi.
e. What did you assume to do these analyses? Demonstrate the validity of your assumptions