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 Captain's exam are the same for all the three races at the 5% significance level.
Test statistic, F: 5.03, 14.12, 9.27, or 5.63? (select one)
P-value: 0.0115, 0.0282, 0.0921, or 0.1936? (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.
One-way ANOVA: Combined results versus Race
Source | DF | SS | MS | F | P |
Race | 2 | 1971.7 | 985.8 | 13.60 | 0.000 |
Error | 115 | 8339.1 | 72.5 | ||
Total | 117 | 10310.8 |
F-value=13.60
P-value=0.000 < 0.001
####
From the give values of F, the nearest to 13.60 is 14.12. Hence, the answer to F=14.12.
P-value =0.0115 (it is the smallest from the given list).
Conclusion: A. Reject the null hypothesis. There is sufficient evidence that at least one mean combined score is different between races.
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