Question

The P-value for the test in Question 5 is $0.0087$. A correct interpretation of this result is that

(a) the probability that there is no linear relationship between an average number of putts per hole and total winnings for these $69$players is $0.0087$.

(b) the probability that there is no linear relationship between the 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 an 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 yields a least-squares regression line with a slope of $-4139198$or less is $0.0087$.

(d) if there is no linear relationship between an 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 yields a least-squares regression line with a slope of $-4139198$or less is $0.0087$.

(e) the probability of making a Type II error is$0.0087$.

Short answer

A correct interpretation of this result is the option (d) if there is no linear relationship between an 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 yields a least-squares regression line with a slope of $-4139198$or less is$0.0087$ .

Step-by-step solution

Given information

Given in the question that, the $P$value for the test is $0.0087$.

We have to find the correct interpretation of the result.

Explanation

The given data is

$H_0:\beta =0$

$H_a:\beta <0$

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme if the null hypothesis is true.

The statement refers to a population and not to a sample.