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 75 69 72 71 71 72 68 68 74
A: First 68 69 60 71 65 71 71 71 71

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

The sample test statistic (t) can be calculated by first finding the mean difference in scores between the final and first rounds, calculating the standard deviation of these differences, dividing the mean by the standard error, and then using the correct degrees of freedom.

Explanation:

To find the value of the sample test statistic, we first need to calculate the mean difference in scores between the final round (row B) and the first round (row A). In this case, we perform paired sample t-test. The t-test will show us if there is a meaningful difference in performance between the two rounds.

Calculate the differences between the two rounds for each player.
Calculate the mean of these differences.
Then find the sample standard deviation (Sd) of these differences.
Finally, the sample test statistic(t) is calculated by dividing the mean by the standard error (mean/Sd/√n).

Note: While doing this, the degrees of freedom will be n-1. If the exact number is not available in the Student's t table, use the closest number that is smaller.

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