Question

Imagine that we conducted a survey and asked individuals about their education and their smoking habits. The results are below. Are these two variables correlated? If so, what are two potential confounding variables that would explain a statistically significant correlation between education and smoking habits? Explain.

	LESS EDUCATED	MORE EDUCATED
HEAVY SMOKER	15	3
LIGHT SMOKER	40	17
NON SMOKER	48	74

Answer 1

Claim: There is a correlation between education and smoking habits.

The null and alternative hypothesis is

H0: There is no correlation between education and smoking habits.

H1: There is a correlation between education and smoking habits.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

	MORE EDUCATED
LESS EDUCATED			Total
HEAVY SMOKER	15	3	18
LIGHT SMOKER	40	17	57
NON SMOKER	48	74	122
Total	103	94	197

O	E	(O-E)	(O-E)^2	(O-E)^2/E
15	9.411168	5.588832	31.23505	3.318935
3	8.588832	-5.58883	31.23505	3.636705
40	29.80203	10.19797	103.9986	3.489648
17	27.19797	-10.198	103.9986	3.823763
48	63.7868	-15.7868	249.2231	3.907127
74	58.2132	15.7868	249.2231	4.281213
			Total	22.457

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (2 - 1) = 2 * 1 = 2

Critical value = 5.991

( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

There is a correlation between education and smoking habits.