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.

Predicted Values For New Observations

New Obs	Fit	SE Fit	​95% CI	​95% PI
1	61.308	0.362	​(60.575​, 62.041	​(56.720, 65.896)

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 ​(_____,_____).

​(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 mean driving accuracy for all golfers driving the ball 300 yards is between the limits of the prediction interval.

B.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.

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 ​(______,_______).

​(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 mean driving accuracy for all golfers driving the ball 300 yards is between the limits of the confidence interval.

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

C.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. If you are interested in knowing the average driving accuracy of all golfers who have a driving distance of 300​ yards, which of the intervals is​ relevant? Explain. Choose the correct answer below.

A.The prediction interval for the single value because it estimates the single value while the confidence interval for the mean estimates the mean.

B.The confidence interval for the mean because it estimates the mean while the prediction interval for the actual value estimates a single​ value, not a mean.

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

Answer 1

a)

The​ 95% prediction interval is (56.720, 65.896)

B.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.

b)

The​ 95% confidence interval is ​ ​(60.575​, 62.041)

A.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.

c) B.The confidence interval for the mean because it estimates the mean while the prediction interval for the actual value estimates a single​ value, not a mean.