A leak of hazardous substance at the Apassney Engineering fa

A leak of hazardous substance at the Apassney Engineering factory threatens the health of the workforce. A random sample of 80 employees had their contamination levels checked. The results were:

Level of contamination           Production                  Administration

High                                        11                                4

Medium                                   24                                10

Low                                         15                                16

Test the hypothesis that there is no association between department and contamination level. Use a 5% level of significance.

Solution

Ho: there is no association between department and contamination level.

H1: there is an association between department and contamination level.

Doing an Expected Value Chart,          
          
9.375   5.625  
21.25   12.75  
19.375   11.625  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    4.334539321      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    3      
          
df =    2      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    5.991464547      
          
Also, the p value is          
          
P =    0.114489787      
          
As chi^2 < 5.991, and P > 0.05,, we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence there is an association between department and contamination level. [CONCLUSION]