# You may need to use the appropriate technology to answer this question. Scores in the first and fourth (final) rounds

###### Question:

You may need to use the appropriate technology to answer this question.

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 73
Golfer 4 72 71
Golfer 5 70 69
Golfer 6 67 67
Golfer 7 71 68
Golfer 8 68 73
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 65
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 =

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.

(c)

What is the margin of error for a 90% confidence interval estimate for the difference between the population means? (Round your answer to two decimal places.)

Could this confidence interval have been used to test the hypothesis in part (a)? Explain.

Yes. One could check to see if the 90% confidence interval includes a difference of 1. If the interval does not contain 1, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of 1. If the interval contains 1, the difference is not statistically significant.    Yes. One could check to see if the 90% confidence interval includes a difference of zero. If the interval does not contain 0, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of zero. If the interval contains 0, the difference is not statistically significant.No. One can not use a confidence interval to test hypothesis in part (a) because hypothesis tests and confidence intervals are two different things.

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