A sample of 500 drivers was asked whether or not they speed

A sample of 500 drivers was asked whether or not they speed while driving. The following table gives a two-way classification: We wish to test whether gender and speeding are related at the 1 % significance level. State the null and alternative hypotheses for this test. Find the critical value for this test. Calculate the test statistic. Should we reject the null hypothesis? Based on your answers to a-d, are gender and speeding likely to be independent?

Solution

a)

Ho: Gender and speeding are independent.
Ha: Gender and speeding are not independent.

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b)

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
Thus, the critical value is          
          
significance level =    0.01      
          
chi^2(critical) =    6.634896601   [ANSWER]

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c)  

Doing an Expected Value Chart,          
          
210   90  
140   60  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    5.714285714   [ANSWER]

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d)

As chi^2 < 6.6349, we fail to reject Ho. [ANSWER, FAIL TO REJECT]

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e)

YES, THEY ARE LIKELY TO BE INDEPENDENT. [ANSWER]  
          
          
Also, the p value is          
          
P =    0.016827409      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that the variables are dependent to each other.