Question

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Do professional golfers play better in their last round? Let row B represent the score in the fourth (and final) round, and let row A represent the score in the first round of a professional golf tournament. A random sample of finalists in the British Open gave the following data for their first and last rounds in the tournament.
B: Last   70   66   72   71   71   72   68   68   74
A: First   70   61   61   71   65   71   71   71   71

Do the data indicate that the population mean score on the last round is higher than that on the first? Use a 5% level of significance. (Let d = B − A.)
(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0: μd = 0; H1: μd ≠ 0; two-tailed
H0: μd = 0; H1: μd < 0; left-tailed
H0: μd = 0; H1: μd > 0; right-tailed
H0: μd > 0; H1: μd = 0; right-tailed

(b) What sampling distribution will you use? What assumptions are you making?
The Student's t. We assume that d has an approximately normal distribution.
The Student's t. We assume that d has an approximately uniform distribution.
The standard normal. We assume that d has an approximately uniform distribution.
The standard normal. We assume that d has an approximately normal distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the P-value.
P-value > 0.250
0.125 < P-value < 0.250
0.050 < P-value < 0.125
0.025 < P-value < 0.050
0.005 < P-value < 0.025
P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence to claim that the population score on the last round is higher than that on the first.
Fail to reject the null hypothesis, there is sufficient evidence to claim that the population score on the last round is higher than that on the first.
Fail to reject the null hypothesis, there is insufficient evidence to claim that the population score on the last round is higher than that on the first.
Reject the null hypothesis, there is insufficient evidence to claim that the population score on the last round is higher than that on the first.

Answer 1