Question

In: Statistics and Probability

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

Complete the table for the combined scores for the Captain's exam.

Race n Mean Std. Dev.
Black 8 (Select one): 63.78, 62.11, 73.28, or 66,27?    (Select one): 8.49, 6.39, 8.31, or 9.27?
Hispanic 8 (Select one): 68.55, 67.19, 62.18, or 65.65? (Select one): 8.70, 9.11, 8.28, or 6.14?   
White 25 (Select one): 74.11, 63.92, 68.54, or 70.09? (Select one): 8.25, 7.38, 8.89, or 8.71?   

Solutions

Expert Solution

Following is the data for the combined scores for the Captain's exam:

B H W
51.304 57.344 56.324
55.8 59.456 60.828
58.192 62.428 62.896
60.648 65.856 67.856
67.152 69.192 69.22
70.38 76.02 69.372
71.828 78.4 69.372
74.952 79.676 69.828
69.952
71.268
71.352
73.6
73.732
75.068
75.724
76.4
76.448
76.916
78.124
79.676
80.876
81.028
85.152
89
92.808

Following is the output of descriptive statistics generated by excel;

Descriptive statistics
B H W
count 8 8 25
mean 63.78200 68.54650 74.11280
sample standard deviation 8.49269 8.70168 8.25184
sample variance 72.12577 75.71930 68.09290
minimum 51.304 57.344 56.324
maximum 74.952 79.676 92.808
range 23.648 22.332 36.484

Answers:

Race n Mean Std. Dev.
Black 8 63.78   8.49
Hispanic 8 68.55 8.70
White 25 74.11 8.25

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