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 PGA tournaments are shown in the following table. Player First Round Final Round Michael Letzig 70 72 Scott Verplank 71 72 D. A. Points 70 75 Jerry Kelly 72 71 Soren Hansen 70 69 D. J. Trahan 67 67 Bubba Watson 71 67 Reteif Goosen 68 75 Jeff Klauk 67 73 Kenny Perry 70 69 Player First Round Final Round Aron Price 72 72 Charles Howell 72 70 Jason Dufner 70 73 Mike Weir 70 77 Carl Pettersson 68 70 Bo Van Pelt 68 65 Ernie Els 71 70 Cameron Beckman 70 68 Nick Watney 69 68 Tommy Armour III 67 71 Suppose you would like to determine if the mean score for the first round of a PGA Tour 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 ? = 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 ?d = mean score first round − mean score fourth round.) H0: ?d ≠ 0 Ha: ?d = 0 H0: ?d = 0 Ha: ?d ≤ 0 H0: ?d > 0 Ha: ?d ≤ 0 H0: ?d ≤ 0 Ha: ?d > 0 H0: ?d = 0 Ha: ?d ≠ 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 sufficient evidence to conclude that the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round.Reject H0. There is insufficient evidence to conclude that the mean score for the first round of a PGA Tour event 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 PGA Tour event 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 PGA Tour event 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 zero. If the interval does not contain zero, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of one. If the interval contains one, 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 zero, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of one. If the interval does not contain one, 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.

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 PGA tournaments are shown in the following table. Player First Round Final Round Michael Letzig 70 72 Scott Verplank 71 72 D. A. Points 70 75 Jerry Kelly 72 71 Soren Hansen 70 69 D. J. Trahan 67 67 Bubba Watson 71 67 Reteif Goosen 68 75 Jeff Klauk 67 73 Kenny Perry 70 69 Player First Round Final Round Aron Price 72 72 Charles Howell 72 70 Jason Dufner 70 73 Mike Weir 70 77 Carl Pettersson 68 70 Bo Van Pelt 68 65 Ernie Els 71 70 Cameron Beckman 70 68 Nick Watney 69 68 Tommy Armour III 67 71 Suppose you would like to determine if the mean score for the first round of a PGA Tour 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 ? = 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 ?d = mean score first round − mean score fourth round.) H0: ?d ≠ 0 Ha: ?d = 0 H0: ?d = 0 Ha: ?d ≤ 0 H0: ?d > 0 Ha: ?d ≤ 0 H0: ?d ≤ 0 Ha: ?d > 0 H0: ?d = 0 Ha: ?d ≠ 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 sufficient evidence to conclude that the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round.Reject H0. There is insufficient evidence to conclude that the mean score for the first round of a PGA Tour event 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 PGA Tour event 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 PGA Tour event 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 zero. If the interval does not contain zero, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of one. If the interval contains one, 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 zero, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of one. If the interval does not contain one, 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are shown in the following table.

Player	First Round	Final Round
Michael Letzig	70	72
Scott Verplank	71	72
D. A. Points	70	75
Jerry Kelly	72	71
Soren Hansen	70	69
D. J. Trahan	67	67
Bubba Watson	71	67
Reteif Goosen	68	75
Jeff Klauk	67	73
Kenny Perry	70	69

Player	First Round	Final Round
Aron Price	72	72
Charles Howell	72	70
Jason Dufner	70	73
Mike Weir	70	77
Carl Pettersson	68	70
Bo Van Pelt	68	65
Ernie Els	71	70
Cameron Beckman	70	68
Nick Watney	69	68
Tommy Armour III	67	71

Suppose you would like to determine if the mean score for the first round of a PGA Tour 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

? = 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 ?_d = mean score first round − mean score fourth round.)

H₀:

?_d ≠ 0

H_a:

?_d = 0

H₀:

?_d = 0

H_a:

?_d ≤ 0

H₀:

?_d > 0

H_a:

?_d ≤ 0

H₀:

?_d ≤ 0

H_a:

?_d > 0

H₀:

?_d = 0

H_a:

?_d ≠ 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 sufficient evidence to conclude that the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round.Reject H₀. There is insufficient evidence to conclude that the mean score for the first round of a PGA Tour event 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 PGA Tour event 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 PGA Tour event 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 zero. If the interval does not contain zero, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of one. If the interval contains one, 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 zero, the difference is not statistically significant.Yes. One could check to see if the 90% confidence interval includes a difference of one. If the interval does not contain one, 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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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