Question

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.6 The P -value for the test in Exercise T12.5 is 0.0087. Which of the following is a correct interpretation of this result?
a. The probability there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b. The probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour’s world money list is 0.0087.
c. If there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
d. If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

Short answer

The correct answer is option (d) If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of $69$ players that yields a least-squares regression line with a slope of $-4,139,198$ or less is $0.0087$.

Step-by-step solution

Given information

To determine the $P$-value for the test in Exercise $T12.5$is $0.0087$.

Explanation

For shooting low scores and hence winning money, it is assumed that good putting is more significant than long driving.A random sample of players is picked for study to see if this is the fact.
They assumed that the slope inference conditions were met, and that the data was calculated using the computer output provided in the question.
Assume the researcher is putting the theory to the test.
The test statistic's P-value is $0.0087$. As a result, it is assumed that
$H_0:\beta =0$
$H_1:\beta <0$
The $P$-value is the probability of obtaining the test statistic's value or a variable that is more excessive if the null hypothesis is true.
It is a population, not a sample, that is mentioned in the sentence.
As a result, the option (d) is the correct option.