Question

Graduation Rates. Refer to Problems 11 and 12

a. Find a point estimate for the mean graduation rate of all universities that have a student-to-faculty ratio of 17 .

b. Determine a 95 % confidence interval for the mean graduation rate of all universities that have a student-to-faculty ratio of 17

Short answer

There is $95\%$ confident that the mean graduation rate of all universities that have a student-tofaculty ratio of 17 lies between 42.60 and 59.18

Step-by-step solution

Step 1:Given information

Step 2:Observation

Find the point estimate for the mean graduation rate of all universities that have a student-tofaculty ratio of 17 by using MINITAB.

MINITAB procedure:

Step 1: ChooseStat > Regression > Regression.

Step 2: In Response, enter the columnGRADRATE.

Step 3: In Predictors, enter the columns SF RATIO.

Step 4: In Options,enter 17 under Prediction interval for new observations,

Step 5: In Confidence Level, enter95 .

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

Step 3:Explaination Part a)

From the MINITAB output, the point estimate for the mean graduation rate of all universities that have a student-to-faculty ratio of 17 is$50.89$

Step 4:Explaination Part b)

Compute the $95\%$confidence interval for the mean graduation rate of all universities that have a student-to-faculty ratio of 17 by using MINITAB.

From the MINITAB output in part (a), the $95\%$confidence interval for the mean graduation rate of all universities that have a student-to-faculty ratio of 17 is $(42.60,59.18)$.