Question

Graduation Rates. Refer to Problems 11 and 12 .

a. Find the predicted graduation rate for a university that has a student-to-faculty ratio of 17 .

b. Find a 95 % prediction interval for the graduation rate of a university that has a student-to-faculty ratio of 17 .

c. Explain why the prediction interval in part (b) is wider than the confidence interval in Problem 15 (b).

Short answer

Part a)The predicted graduation rate for a university that has a student-tofaculty ratio of 17 is 50.89

Part b)The graduation rate of a university that has a student-to-faculty ratio of 17 lies between 23.53 % and 78.25 %

Part c)The confidence interval and the prediction interval are centered at the predicted value for student-to-faculty of 17

Step-by-step solution

Step 1:Given information

Step 2:Explaination Part a)

Find the predicted graduation rate for a university that has a student-to-faculty ratio of 17 by using MINITAB.

MINITAB procedure:

Step 1: Choose Stat > Regression > Regression.

Step 2: In Response, enter the columnGRADRATE.

Step 3: InPredictors, enter the columns SF RATIO.

Step 4: InOptions, enter 17 under Prediction interval for new observations.

Step 5: In Confidence Level, enter 95 .

Step 6: In Storage, Choose Fits, Confidence limits, SEs of fits, and Prediction limits.

Step 7: Click OK.

MINITAB output:

Predicted Values for New Observations

From the MINITAB output, the predicted graduation rate for a university that has a student-tofaculty ratio of 17 is 50.89

Step 2:EXplaination Part b)

Find a 95 % prediction interval for the graduation rate of a university that has a student-to-faculty ratio of 17 by using MINITAB.

From the MINITAB output in part (a), the 95 % prediction interval for the graduation rate of a university that has a student-to-faculty ratio of 17 is (23.53,78.25)

Interpretation:

There is 95 % certain that the graduation rate of a university that has a student-to-faculty ratio of 17 lies between 23.53 % and 78.25 %

Step 2:Explaination Part c)

The prediction interval in part (b) is wider than the confidence interval because the prediction interval is more helpful to forecast the future observation but the confidence interval estimates the parameter. Moreover, the confidence interval and the prediction interval are centered at the predicted value for student-to-faculty of 17 .