Exercise 2

1. Refer to the grade point average (GPA) problem (problem 1 Exercise 1). The results are in file GPA and a brief description of the variables is in the file GPAd.

  1. Obtain a 99 percent confidence interval for b1. Interpret your confidence interval. Does it include zero? Why should the director of admission be interested in whether the confidence interval includes zero?

  2. Test, using the t-statistics, whether of not a linear relationship exists between the entrance score (X) and the GPA score (Y). Use a level of significance of 0.01. State the alternatives, decision rule and conclusion.

  3. What is the p-value of your test in the previous question? How does it support the conclusion reached in the previous question?

 

2. Refer again to the grade point average (GPA) problem (problem 1 Exercise 1).

  1. Obtain a 95 percent confidence interval for the mean freshman GPA for students whose entrance score is 4.7. Interpret your confidence interval.

  2. Moshe Shemesh obtained an entrance score is 4.7. Predict his freshman GPA using a 95 percent prediction interval Interpret your prediction interval.

  3. Is the prediction interval in question b. wider than the confidence interval in question a.? Should it be?

 

3. Refer now to the AirFreight Breakage problem (problem 3 Exercise 1). The data are in file AIRFREIGHT and a brief description of the variables is in the file AIRFRd.

  1. Because of changes of airline routes, shipments may have to be transferred more frequently than in the past. Estimate the mean breakage for the following number of transfers: X=2, 4. Use separate 95 percent confidence intervals. Interpret your results.

  2. The next shipments will have two transfers. Obtain a 95 percent prediction interval for the number of ampules found broken in this shipment. Interpret your prediction interval.

  3. In the next several days, three independent shipments will be made, each having two transfers. Obtain a 99 percent prediction interval for the mean number of ampules broken in the three shipments. Convert this interval into a 99 percent prediction interval for the total number of ampules broken in the three shipments.

 

4. Refer now to the Muscle Mass problem (problem 2 Exercise 1). The results are in file MUSCLE and a brief description of the variables is in the file MUSCLEd. X is the age and Y is a measure of muscle mass.

  1. Conduct a test to decide whether or not there is a negative linear association between the amount of a person's muscle mass and age. Control the risk of Type I error at 0.05. State the alternatives, decision rule and conclusion. What is the p-value of the test?

  2. Obtain a 95 percent confidence interval for b0. Can it be concluded that b0 provides relevant information on the amount of muscle mass at birth for a female child?

  3. Estimate with a 95 percent confidence interval the difference in the expected muscle mass for women whose age differ by one year. Why is it not necessary to know the specific ages to make this estimate?