The modulus of rupture (MOR) for the specific grade of pencil lead is known to have the standard deviation of 250 psi. Process standards call for target value of 6500 psi for true mean MOR. For each batch, an inspector tests the random sample of 16 leads. Management wishes to detect any change in the true mean MOR.
a. A recent random sample yielded the sample mean of 6490 psi. Conduct an hypothesis test to find out whether the true mean MOR has changed from the 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. Describe the relationship of the 90% confidence interval and the corresponding hypothesis test.
c. Determine the power of this test to detect a change in the true mean MOR to 6400 psi.
d. Determine the sample size required to achieve an approximate power of 0.85 when the true mean MOR is 6400 psi.
e. What did you suppose to do these analyses? Demonstrate the validity of your assumptions.