Data: (if needed) Race Position Oral exam results Written exam results Combined results B Lieutenant 45.83 ...

Data: (if needed)

Race   Position   Oral exam results   Written exam results   Combined results
B   Lieutenant   45.83   46   45.932
B   Lieutenant   52.92   49   50.568
B   Captain   54.76   49   51.304
H   Lieutenant   48.33   58   54.132
B   Lieutenant   52.08   56   54.432
H   Lieutenant   40.83   64   54.732
B   Captain   60   53   55.8
W   Captain   53.81   58   56.324
B   Lieutenant   58.75   55   56.5
W   Lieutenant   54.58   58   56.632
B   Lieutenant   55.83   58   57.132
W   Lieutenant   45.42   65   57.168
H   Lieutenant   44.17   66   57.268
H   Captain   42.86   67   57.344
W   Lieutenant   44.58   66   57.432
W   Lieutenant   51.25   62   57.7
W   Lieutenant   57.92   58   57.968
B   Captain   70.48   50   58.192
B   Lieutenant   60.83   58   59.132
H   Lieutenant   46.25   68   59.3
H   Captain   57.14   61   59.456
W   Lieutenant   60   60   60
W   Lieutenant   49.58   67   60.032
B   Lieutenant   51.25   66   60.1
B   Lieutenant   55   64   60.4
B   Captain   67.62   56   60.648
H   Lieutenant   51.25   67   60.7
H   Lieutenant   42.5   73   60.8
W   Captain   48.57   69   60.828
B   Lieutenant   56.25   64   60.9
B   Lieutenant   56.67   64   61.068
W   Lieutenant   56.25   66   62.1
H   Captain   58.57   65   62.428
H   Lieutenant   50.42   71   62.768
W   Lieutenant   71.67   57   62.868
W   Captain   55.24   68   62.896
H   Lieutenant   51.67   71   63.268
B   Lieutenant   69.17   60   63.668
H   Lieutenant   57.5   70   65
W   Lieutenant   50.42   75   65.168
B   Lieutenant   66.25   65   65.5
W   Lieutenant   55   73   65.8
H   Captain   67.14   65   65.856
H   Lieutenant   56.25   73   66.3
W   Lieutenant   79.17   59   67.068
B   Captain   52.38   77   67.152
W   Lieutenant   64.58   69   67.232
B   Lieutenant   70.83   65   67.332
W   Captain   57.14   75   67.856
W   Lieutenant   51.67   79   68.068
H   Lieutenant   62.5   72   68.2
W   Lieutenant   51.25   80   68.5
W   Lieutenant   73.75   66   69.1
W   Lieutenant   58.75   76   69.1
H   Lieutenant   70.83   68   69.132
H   Captain   60.48   75   69.192
W   Captain   59.05   76   69.22
W   Captain   71.43   68   69.372
W   Captain   71.43   68   69.372
W   Lieutenant   64.58   73   69.632
W   Captain   78.57   64   69.828
W   Captain   62.38   75   69.952
W   Lieutenant   71.67   69   70.068
W   Lieutenant   73.75   68   70.3
B   Captain   70.95   70   70.38
W   Lieutenant   77.5   66   70.6
H   Lieutenant   53.75   82   70.7
W   Lieutenant   65.83   74   70.732
W   Lieutenant   58.33   79   70.732
H   Lieutenant   69.17   72   70.868
H   Lieutenant   55   82   71.2
W   Captain   56.67   81   71.268
W   Captain   82.38   64   71.352
B   Captain   68.57   74   71.828
W   Lieutenant   73.33   71   71.932
W   Lieutenant   72.5   72   72.2
B   Lieutenant   92.08   59   72.232
W   Lieutenant   66.67   76   72.268
B   Lieutenant   70.83   74   72.732
W   Lieutenant   78.33   70   73.332
W   Captain   70   76   73.6
W   Captain   73.33   74   73.732
B   Lieutenant   65.83   80   74.332
W   Lieutenant   87.5   66   74.6
B   Captain   82.38   70   74.952
W   Captain   76.67   74   75.068
W   Lieutenant   63.33   83   75.132
W   Captain   73.81   77   75.724
W   Lieutenant   74.17   77   75.868
B   Lieutenant   80.42   73   75.968
H   Captain   79.05   74   76.02
B   Lieutenant   61.25   86   76.1
W   Captain   80   74   76.4
W   Captain   87.62   69   76.448
B   Lieutenant   77.5   76   76.6
W   Lieutenant   58.75   89   76.9
W   Captain   84.29   72   76.916
W   Lieutenant   73.75   81   78.1
W   Captain   73.81   81   78.124
H   Captain   70   84   78.4
W   Lieutenant   69.58   86   79.432
W   Captain   76.19   82   79.676
H   Captain   76.19   82   79.676
W   Captain   76.19   84   80.876
W   Captain   88.57   76   81.028
W   Lieutenant   68.33   91   81.932
W   Lieutenant   63.75   95   82.5
W   Lieutenant   80.83   84   82.732
W   Lieutenant   73.33   89   82.732
W   Lieutenant   73.75   91   84.1
W   Lieutenant   80   87   84.2
W   Lieutenant   85   84   84.4
W   Captain   82.38   87   85.152
W   Lieutenant   77.5   91   85.6
W   Lieutenant   87.5   87   87.2
W   Captain   80   95   89
W   Lieutenant   88.75   91   90.1
W   Captain   89.52   95   92.808

Test whether the combined test scores for the Lieutenant exam are the same for all the three races at the 5% significance level.

Test statistic, F: 8.58, 12.09, 6.84, or 8.01? (select one)

P-value: 0.004, 0.963, 0.084, or 0.027? (select one)

Conclusion: A. Reject the null hypothesis. There is sufficient evidence that at least one mean combined score is different between races.

B. Reject the null hypothesis. There is insufficient evidence that at least one mean combined score is different between races.

C. Fail to reject the null hypothesis. There is sufficient evidence that at least one mean combined score is different between races.

D. Fail to reject the null hypothesis. There is insufficient evidence that at least one mean combined score is different between races.

Expert Solution

Following is the data set for combined results for Lieutenant for different races:

B	H	W
45.932	54.132	56.632
50.568	54.732	57.168
54.432	57.268	57.432
56.5	59.3	57.7
57.132	60.7	57.968
59.132	60.8	60
60.1	62.768	60.032
60.4	63.268	62.1
60.9	65	62.868
61.068	66.3	65.168
63.668	68.2	65.8
65.5	69.132	67.068
67.332	70.7	67.232
72.232	70.868	68.068
72.732	71.2	68.5
74.332		69.1
75.968		69.1
76.1		69.632
76.6		70.068
		70.3
		70.6
		70.732
		70.732
		71.932
		72.2
		72.268
		73.332
		74.6
		75.132
		75.868
		76.9
		78.1
		79.432
		81.932
		82.5
		82.732
		82.732
		84.1
		84.2
		84.4
		85.6
		87.2
		90.1

Following is the output generated by excel:

One factor ANOVA

	Mean	n	Std. Dev
	63.7173	19	9.07690	B
	63.6245	15	5.76888	H
	71.8433	43	9.14592	W
	68.2371	77	9.40928	Total

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	1,266.47361	2	633.236807	8.58	.0004
Error	5,462.15146	74	73.812858
Total	6,728.62508	76

That is,

Test statistics: F = 8.58

The p-value: 0.0004

Since p-value is less than 0.05 so we reject the null hypothesis.

Correct option is:

A. Reject the null hypothesis. There is sufficient evidence that at least one mean combined score is different between races.

orchestra answered 1 year ago

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