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Chapter 14: Q 15 (page 588)

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

Expert verified

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

01

Step 1:Given information

02

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

03

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 is50.89

04

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).

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Most popular questions from this chapter

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(h).
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a 95% confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a 95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).

14.101 Acreage and Value. The data from Exercise 14.37for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site. Specified value of the predictor variable: 2.5 acres.

Gas Guzzlers. The data from Exercise 14.41 for gas mileage and engine displacement of 121 vehicles are on the WeissStats site. Specified value of the predictor variable: 3.0L.

a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(f).

b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

c. Find and interpret a 95%confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.

e. Find and interpret a 95%prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).

In Exercises 14.12-14.21, we repeat the data and provide the sample regression equations for Exercises 4.48 -4.57.

a. Determine the standand error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

Find a 95%prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

To find and interpret a confidence interval , at the specified confidence level90% for the slope of the population regression line that relates the response variables to the predictor variable.
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