Using the data below, test whether education and smoking status are independent.
ID: 3388150 • Letter: U
Question
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
Smoker
Non-Smoker
High School Graduate
12
38
< 4 years of college
45
152
Bachelor’s Degree
32
239
Graduate Degree
5
52
Explanation / Answer
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]
******************************
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]
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