The following table gives the twoway classification of 400 r

The following table gives the two-way classification of 400 randomly selected persons based on their smoking habits, and the number of visits to the physicians last year: Is there sufficient evidence that the number of visits to the physician depends upon the smoking habits? Use alpha= 0.05

Solution

Doing an Expected Value Chart,          
          

0-1 2-4 5 or more
Smoker 54   60   46  
Nonsmoker 81   90   69  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    56.42780462 [TEST STATISTIC]      
          
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   [CRITICAL VALUE]  
          
As chi^2 > 5.99146, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that the number of visits to the physician depends upon the smoking habits. [CONCLUSION]