Question

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 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.   

Homework Answers

Answer #1

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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