Question

You may need to use the appropriate technology to answer this 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 8,818 Lehigh Valley IronPigs North 55 89 0.382 8,471 Pawtucket Red Sox North 85 58 0.594 9,095 Rochester Red Wings North 74 70 0.514 6,918 Scranton-Wilkes Barre Yankees North 88 56 0.611 7,144 Syracuse Chiefs North 69 73 0.486 5,764 Charlotte Knights South 63 78 0.447 4,522 Durham Bulls South 74 70 0.514 6,997 Norfolk Tides South 64 78 0.451 6,283 Richmond Braves South 63 78 0.447 4,459 Columbus Clippers West 69 73 0.486 7,791 Indianapolis Indians West 68 76 0.472 8,531 Louisville Bats West 88 56 0.611 9,156 Toledo Mud Hens West 75 69 0.521 8,235 (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: Not all the population means are equal. Ha: μN = μS = μW H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: μN ≠ μS ≠ μW Ha: μN = μS = μW H0: μN = μS = μW Ha: μN ≠ μS ≠ μW H0: μN = μS = μW Ha: Not all the population means are equal. Correct: Your answer is correct. Find the value of the test statistic. (Round your answer to two decimal places.) 6.95 Correct: Your answer is correct. Find the p-value. (Round your answer to three decimal places.) p-value = .0111 Correct: Your answer is correct. State your conclusion. 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. Reject H0. There is not sufficient evidence to conclude that the mean attendance values are not equal for the three divisions. Correct: Your answer is correct. (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 South LSD = Incorrect: Your answer is incorrect. North and West LSD = South and West LSD = Find the pairwise absolute difference between sample attendance means for each pair of divisions. (Round your answers to the nearest integer.) xN − xS = 2136 Correct: Your answer is correct. xN − xW = 727 Correct: Your answer is correct. xS − xW = 2863 Correct: Your answer is correct. 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. Correct: Your answer is correct.

Answer 1

(a)

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

North	South	West		Anova: Single Factor
8818	4522	7791
8471	6997	8531		SUMMARY
9095	6283	9156		Groups	Count	Sum	Average	Variance
6918	4459	8235		Column 1	6	46210	7701.667	1691826
7144				Column 2	4	22261	5565.25	1625744
5764				Column 3	4	33713	8428.25	327870.3
				ANOVA
				Source of Variation	SS	df	MS	F	P-value	F crit
				Between Groups	18097221	2	9048610	6.950761	0.011179	3.982298
				Within Groups	14319973	11	1301816
				Total	32417194	13

Value of the test statistic= 6.95

p-value= 0.011

Since p-value<0.05 so

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

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.