Question

A group of researchers developed a new method for ranking the total driving performance of golfers on a tour. The method requires knowing a​ golfer's average driving distance​ (yards) and driving accuracy​ (percent of drives that land in the​ fairway). They construct a​ straight-line model relating driving accuracy​ (y) to driving distance​ (x). A MINITAB printout with prediction and confidence intervals for a driving distance of x=300 is shown below

MINITAB output

Predicted Values For New Observations

New Obs	Fit	SE Fit	​95% CI	​95% PI
1	61.303	0.359	​(60.576, 62.030)	​(56.716)​, 65.890)

Values of Predictors for New Observations

New Obs	DISTANCE
1	300

a. Locate the​ 95% prediction interval for driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result.

The​ 95% prediction interval is ​(56.716,65.890).​(Round to three decimal places as​ needed.)

Give a practical interpretation of the result. Choose the correct answer below.

A.We are​ 95% confident that the actual driving accuracy for a golfer driving the ball 300 yards is between the limits of the prediction interval.THIS answer is correct.

B.We are​ 95% confident that the mean driving accuracy for all golfers driving the ball 300 yards is between the limits of the prediction interval.

C.There is not enough information to answer this question.

b. Locate the​ 95% confidence interval for mean driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result.

The​ 95% confidence interval is ​(60,576​,62.030). ​(Round to three decimal places as​ needed.)

Give a practical interpretation of the result. Choose the correct answer below.

A. There is not enough information to answer this question.

B.We are​ 95% confident that the actual driving accuracy for a golfer driving the ball 300 yards is between the limits of the confidence interval.

C.We are​ 95% confident that the mean driving accuracy for all golfers driving the ball 300 yards is between the limits of the confidence interval.

Answer 1

% Answer

First of all, we have to understand the difference between prediction interval and confidence interval. Prediction interval is used for predicting the mean value range for the next single new observation whereas the confidence interval is used to predict about the population mean.

(a) Prediction interval is (56.716,65.890), so we are 95% confident that the actual driving accuracy for a new or next golfer driving the ball 300 yards is between the limits of the prediction interval. Option A is providing the correct statement for a single new value. So, option A is correct

(b) Confidence interval is ​(60,576​,62.030),so we are 95% confident that the population mean driving accuracy for all golfers driving the ball 300 yards is between the limits of the confidence interval. Option C is providing correct statement for the population mean. So, opton C is correct.