Statistics hypothesis test question Many states now collect

Statistics hypothesis test question?

Many states now collect data on traffic stops regarding the race of the driver. With more data in hand attention has turned to civil rights issues. Example, data from 2533 traffic stops in Cincinnati report the race of the driver (Black, White, or Other) and whether the traffic stop resulted in a search of the vehicle. Is race a factor in vehicle searches? At =0.05, what conclusion can we make? (Adapted from: STATS Data and Models, 8^th edition).

Searched

Black

White

Other

Total

No

787

594

27

1408

Yes

813

293

19

1125

Total

1600

887

46

2533

H_o:                                                                   H_a:

Critical Value(s)/rejection region(s):

Test Statistic:

P-value:

Decision and conclusion:

Solution

Here,

Ho: Traffic stops is independent of race.
Ha: Traffic stops is not independent of race.

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With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    3      
b =    2      
          
df =    2      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    5.991464547   [ANSWER, CRITICAL VALUE]

Thus, reject Ho when chi^2 > 5.9915.   [ANSWER, REJECTION REGION]

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Doing an Expected Value Chart,          
          
889.3801816   493.0501382   25.56968022  
710.6198184   393.9498618   20.43031978  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    73.25312847   [ANSWER, TEST STATISTIC]

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Also, the p value is          
          
P =    1.23961*10^-16   [ANSWER]

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As chi^2 > 5.9915, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that traffic stops is not independent of race. [CONCLUSION]