Using the data below test whether education and smoking stat

Using the data below, test whether education and smoking status are independent. Run the test at a 5% level of significance. 1) Write out the appropriate null hypothesis and the alternative hypothesis; 2) Calculate the test statistic; 3) Give your conclusion including a comparison to alpha or the critical value.

Smoker  

Non-Smoker

High School Graduate

12

38

< 4 years of college

45

152

Bachelor’s Degree

32

239

Graduate Degree

5

52

Solution

Here,

Ho: Education and smoking status are independent.
Ha: Education and smoking status are not independent.

Doing an Expected Value Chart,          
          
8.173913043   41.82608696
32.20521739   164.7947826
44.3026087   226.6973913
9.31826087   47.68173913
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    14.69381895   [ANSWER, TEST STATISTIC]

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With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    4      
          
df =    3      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    7.814727903      
          
Also, the p value is          
          
P =    0.002097908      
          
As chi^2 > 7.8147, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that education and smoking status are not independent. [CONCLUSION]