Question

The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 27 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 27 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is -2.18 strokes and the standard deviation of the differences is 8.276 strokes. The owner uses this information to calculate the 95% confidence paired t-interval of (-5.454, 1.094). Which statement is the correct interpretation of this interval? 1 We are 95% confident that the average difference in scores between the two courses for all golfers is between -5.454 and 1.094. 2) The proportion of all golfers that had a difference in scores between the two courses is 95%. 3) We are certain the average difference in scores between the two courses for all golfers is between -5.454 and 1.094. 4 We are 95% confident that the difference between the average score on the owner's golf course and the average score on the friend's golf course is between -5.454 and 1.094. 5) We are 95% confident that the average difference in the scores of the golfers sampled is between -5.454 and 1.094.

Answer 1

Answer:

1) We are 95% confident that the average difference in scores between the two courses for all golfers is between -5.454 and 1.094.

Explanation:

The 95% Confidence interval for the average difference is given as (-5.454, 1.094). This indicates that this confidence interval is for population difference in scores between the two courses for all golfers, not only for sampled golfers.