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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 equals 300  is shown below.

Minitab Output

Predicted values for new observations

Minitab output table
New observation Fit SE Fit 95% CI 95% PI
1       61.303  0.358 (60.578, 62.028) (56.717, 65.889)

I will appreciate assistance in the following questions.

  • Locate the 95% prediction interval for driving accuracy (y) on the printout, and give a practical interpretation of the result.
  • Locate the 95% confidence interval for mean driving accuracy (y) on the printout, and give a practical interpretation of the result.
  • Give a practical interpretation of the result. Choose the correct answer below.
  • 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​ 95% prediction interval is (56.717,​​​​​​​65.889​).

 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.

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 ​(​​​​​​​60.578​,​​​​​​​62.028​).

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.

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.

 

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