Do professional golfers play better in their first 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:

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.
Please provide the following information.
(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?
(b) What sampling distribution will you use? What assumptions are you making? Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.
Assume that the distribution of differences is approximately normal.

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B: Last 7368 73 71 7 72668 74 A: First 6670 64 7 657 71 771