Question

To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.

Machine 1	Machine 2	Machine 3	Machine 4
6.7	8.8	10.8	9.6
7.9	7.6	10.2	12.6
5.6	9.5	9.6	11.9
7.5	10.2	10.1	10.5
8.6	9.4	8.9	11.2
7.5	10.3	8.6	11.4

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

Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a 0.05 level of significance.

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

LSD = ___

Find the pairwise absolute difference between sample means for machines 2 and 4

x₂ − x₄ =___

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	8,479
Pawtucket Red Sox	North	85	58	0.594	9,092
Rochester Red Wings	North	74	70	0.514	6,911
Scranton-Wilkes Barre Yankees	North	88	56	0.611	7,149
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	6,999
Norfolk Tides	South	64	78	0.451	6,287
Richmond Braves	South	63	78	0.447	4,458
Columbus Clippers	West	69	73	0.486	7,799
Indianapolis Indians	West	68	76	0.472	8,537
Louisville Bats	West	88	56	0.611	9,152
Toledo Mud Hens	West	75	69	0.521	8,238

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 =___

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=

Answer 1

1)

Applying ANOVA:

value of the test statistic =15.97

p value =0.000

Fisher's (LSD) for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =

1.19

x2-x4

1.90

significant difference

2)

value of the test statistic =6.95

p value =0.011

North and SouthLSD=1621.56

North and WestLSD=1621.56

South and WestLSD=1776.33

x_N − x_S=2136

x_N − x_W=729

x_S − x_W=2865