The International League of Triple-A minor league baseball consists of 14 teams organized into three divisions: North, South, and West. Suppose the following data show the average attendance for the 14 teams in the International League. Also shown are the teams' records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won. Team Name Division W L PCT Attendance Buffalo Bisons North 66 77 0.462 8,813 Lehigh Valley IronPigs North 55 89 0.382 8,479 Pawtucket Red Sox North 85 58 0.594 9,099 Rochester Red Wings North 74 70 0.514 6,917 Scranton-Wilkes Barre Yankees North 88 56 0.611 7,149 Syracuse Chiefs North 69 73 0.486 5,766 Charlotte Knights South 63 78 0.447 4,524 Durham Bulls South 74 70 0.514 6,994 Norfolk Tides South 64 78 0.451 6,283 Richmond Braves South 63 78 0.447 4,451 Columbus Clippers West 69 73 0.486 7,796 Indianapolis Indians West 68 76 0.472 8,535 Louisville Bats West 88 56 0.611 9,155 Toledo Mud Hens West 75 69 0.521 8,238 (a) Use ? = 0.05 to test for any difference in the mean attendance for the three divisions. State the null and alternative hypotheses. -H0: At least two of the population means are equal. Ha: At least two of the population means are different. -H0: ?N = ?S = ?W Ha: ?N ≠ ?S ≠ ?W -H0: Not all the population means are equal. Ha: ?N = ?S = ?W -H0: ?N = ?S = ?W Ha: Not all the population means are equal. -H0: ?N ≠ ?S ≠ ?W Ha: ?N = ?S = ?W Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. Reject H0. There is not sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.Reject H0. There is sufficient evidence to conclude that the mean attendance values are not equal for the three divisions. Do not reject H0. There is not sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.Do not reject H0. There is sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.

The International League of Triple-A minor league baseball consists of 14 teams organized into three divisions: North, South, and West. Suppose the following data show the average attendance for the 14 teams in the International League. Also shown are the teams' records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won. Team Name Division W L PCT Attendance Buffalo Bisons North 66 77 0.462 8,813 Lehigh Valley IronPigs North 55 89 0.382 8,479 Pawtucket Red Sox North 85 58 0.594 9,099 Rochester Red Wings North 74 70 0.514 6,917 Scranton-Wilkes Barre Yankees North 88 56 0.611 7,149 Syracuse Chiefs North 69 73 0.486 5,766 Charlotte Knights South 63 78 0.447 4,524 Durham Bulls South 74 70 0.514 6,994 Norfolk Tides South 64 78 0.451 6,283 Richmond Braves South 63 78 0.447 4,451 Columbus Clippers West 69 73 0.486 7,796 Indianapolis Indians West 68 76 0.472 8,535 Louisville Bats West 88 56 0.611 9,155 Toledo Mud Hens West 75 69 0.521 8,238 (a) Use ? = 0.05 to test for any difference in the mean attendance for the three divisions. State the null and alternative hypotheses. -H0: At least two of the population means are equal. Ha: At least two of the population means are different. -H0: ?N = ?S = ?W Ha: ?N ≠ ?S ≠ ?W -H0: Not all the population means are equal. Ha: ?N = ?S = ?W -H0: ?N = ?S = ?W Ha: Not all the population means are equal. -H0: ?N ≠ ?S ≠ ?W Ha: ?N = ?S = ?W Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. Reject H0. There is not sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.Reject H0. There is sufficient evidence to conclude that the mean attendance values are not equal for the three divisions. Do not reject H0. There is not sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.Do not reject H0. There is sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.

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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Team Name	Division	W	L	PCT	Attendance
Buffalo Bisons	North	66	77	0.462	8,813
Lehigh Valley IronPigs	North	55	89	0.382	8,479
Pawtucket Red Sox	North	85	58	0.594	9,099
Rochester Red Wings	North	74	70	0.514	6,917
Scranton-Wilkes Barre Yankees	North	88	56	0.611	7,149
Syracuse Chiefs	North	69	73	0.486	5,766
Charlotte Knights	South	63	78	0.447	4,524
Durham Bulls	South	74	70	0.514	6,994
Norfolk Tides	South	64	78	0.451	6,283
Richmond Braves	South	63	78	0.447	4,451
Columbus Clippers	West	69	73	0.486	7,796
Indianapolis Indians	West	68	76	0.472	8,535
Louisville Bats	West	88	56	0.611	9,155
Toledo Mud Hens	West	75	69	0.521	8,238

(a)

Use ? = 0.05 to test for any difference in the mean attendance for the three divisions.

State the null and alternative hypotheses.

-H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

-H₀: ?_N = ?_S = ?_W
H_a: ?_N ≠ ?_S ≠ ?_W

-H₀: Not all the population means are equal.
H_a: ?_N = ?_S = ?_W

-H₀: ?_N = ?_S = ?_W
H_a: Not all the population means are equal.

-H₀: ?_N ≠ ?_S ≠ ?_W
H_a: ?_N = ?_S = ?_W

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

Find the p-value. (Round your answer to three decimal places.)

p-value = ??

State your conclusion.

Reject H₀. There is not sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.Reject H₀. There is sufficient evidence to conclude that the mean attendance values are not equal for the three divisions. Do not reject H₀. There is not sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.Do not reject H₀. There is sufficient evidence to conclude that the mean attendance values are not equal for the three divisions.

(b)

Use Fisher's LSD procedure to determine where the differences occur. Use ? = 0.05.

Find the value of LSD for each pair of divisions. (Round your answers to two decimal places.)

North and SouthLSD=??

North and WestLSD=??

South and WestLSD=??

Find the pairwise absolute difference between sample attendance means for each pair of divisions. (Round your answers to the nearest integer.)

x_N − x_S=??

x_N − x_W=??

x_S − x_W=??

Which attendance means differ significantly? (Select all that apply.)

-There is a significant difference in mean attendance between the North division and the South division.

-There is a significant difference in mean attendance between the North division and the West division.

-There is a significant difference in mean attendance between the South division and the West division.

-There are no significant differences.

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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