In: Statistics and Probability
Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tournaments are shown in the following table.
Player | First Round |
Final Round |
---|---|---|
Golfer 1 | 70 | 72 |
Golfer 2 | 71 | 72 |
Golfer 3 | 70 | 75 |
Golfer 4 | 72 | 71 |
Golfer 5 | 70 | 69 |
Golfer 6 | 67 | 67 |
Golfer 7 | 71 | 67 |
Golfer 8 | 68 | 75 |
Golfer 9 | 67 | 73 |
Golfer 10 | 70 | 69 |
Player | First Round |
Final Round |
---|---|---|
Golfer 11 | 72 | 72 |
Golfer 12 | 72 | 70 |
Golfer 13 | 70 | 73 |
Golfer 14 | 70 | 77 |
Golfer 15 | 68 | 70 |
Golfer 16 | 68 | 66 |
Golfer 17 | 71 | 70 |
Golfer 18 | 70 | 68 |
Golfer 19 | 69 | 68 |
Golfer 20 | 67 | 71 |
Suppose you would like to determine if the mean score for the first round of a golf tournament event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?
(a)
Use
α = 0.10
to test for a statistically significantly difference between the population means for first- and fourth-round scores.
State the null and alternative hypotheses. (Use μd = mean score first round − mean score fourth round.)
H0:
μd = 0
Ha:
μd ≠ 0
H0:
μd > 0
Ha:
μd ≤ 0
H0:
μd ≠ 0
Ha:
μd = 0
H0:
μd = 0
Ha:
μd ≤ 0
H0:
μd ≤ 0
Ha:
μd > 0
Calculate the value of the test statistic. (Round your answer to three decimal places.)
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Reject H0. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.Do not Reject H0. There is sufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round. Do not reject H0. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.Reject H0. There is sufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.
(b)
What is the point estimate of the difference between the two population means? (Use mean score first round − mean score fourth round.)
For which round is the population mean score lower?
The mean of the fourth round scores was lower than the mean of the first round scores.The mean of the first round scores was lower than the mean of the fourth round scores.
Please show your work
Do not reject H0. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.
b) The point estimate of the difference between the two population means is
Since first round mean score is lower.
The mean of the first round scores was lower than the mean of the fourth round scores.