The modulus of rupture (MOR) for a specific grade of pencil lead is known to have standard deviation of 250 psi. Process standards call for a target value of 6500 psi for the true mean MOR. For each and every batch, an inspector tests random sample of 16 leads. Management wishes to detect any change in true mean MOR.
a. A current random sample yielded a sample mean of 6490 psi. Conduct an hypothesis test to find out whether the true mean MOR has changed from target. Employ a 0.10 significance level.
b. Develop a 90% confidence interval for this situation. Employ this interval to find out whether the true mean MOR has changed. Explain the relationship of the 90% confidence interval and the corresponding hypothesis test.