Question

 

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	8,817
Lehigh Valley IronPigs	North	55	89	0.382	8,472
Pawtucket Red Sox	North	85	58	0.594	9,099
Rochester Red Wings	North	74	70	0.514	6,911
Scranton-Wilkes Barre Yankees	North	88	56	0.611	7,143
Syracuse Chiefs	North	69	73	0.486	5,764
Charlotte Knights	South	63	78	0.447	4,521
Durham Bulls	South	74	70	0.514	6,997
Norfolk Tides	South	64	78	0.451	6,282
Richmond Braves	South	63	78	0.447	4,455
Columbus Clippers	West	69	73	0.486	7,796
Indianapolis Indians	West	68	76	0.472	8,536
Louisville Bats	West	88	56	0.611	9,156
Toledo Mud Hens	West	75	69	0.521	8,232

(a)

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

State the null and alternative hypotheses.

H₀: μ_N = μ_S = μ_W
H_a: μ_N ≠ μ_S ≠ μ_WH₀: Not all the population means are equal.
H_a: μ_N = μ_S = μ_W    H₀: μ_N ≠ μ_S ≠ μ_W
H_a: μ_N = μ_S = μ_WH₀: μ_N = μ_S = μ_W
H_a: Not all the population means are equal.H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

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

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.Do not 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.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 α = 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.

Answer 1

Que.a

Hypothesis:

H₀: μ_N = μ_S = μ_W
H_a: Not all the population means are equal

I used MINITAB software to solve this question. Go through following steps:

Step.1 Enter data in minitab as shown in screen shot.                     

Step.2 Go to ‘Stat’ menu ---> ‘ANOVA’ ---> ‘One way ANOVA’

Step.3 New window will-pop on screen. Refer following screen shot and enter information accordingly.

Minitab output:

Factor Information

Factor Levels Values
Factor 3 North, South, West

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 18130636 9065318 6.95 0.011
Error 11 14347949 1304359
Total 13 32478585

Fisher Pairwise Comparisons

Grouping Information Using the Fisher LSD Method and 95% Confidence

Factor N Mean Grouping
West 4 8430 A
North 6 7701 A
South 4 5564 B

Means that do not share a letter are significantly different.

Fisher Individual Tests for Differences of Means

Difference of Difference SE of Adjusted
Levels of Means Difference 95% CI T-Value P-Value
South - North -2137 737 (-3760, -515) -2.90 0.014
West - North 729 737 ( -894, 2352) 0.99 0.344
West - South 2866 808 ( 1089, 4644) 3.55 0.005

Test statistic, F = 6.95

P-value = 0.011

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

Que.b.

Pairwise absolute difference:

Difference of Difference
Levels of Means
South - North -2137
West - North 729
West - South 2866

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 South division and the West division.