Question

One hundred randomly selected subjects from 51,048 subjects were interviewed as a part of the California Health Interview Survey. The table below was constructed from the responses of the 100 subjects. Use a 0.05 significance level to test the claim that for California adults, exercise is independent of gender.

Have you exercised vigorously in the last 7 days?

	YES	NO
MALE	13	34
FEMALE	15	38

Answer 1

Null hypothesis:Ho:   Exercise and Gender are independent.

alternate hypothesis:Ha: Exercise and Gender are dependent.

degree of freedom(df) =(rows-1)*(columns-1)=		1
for 1 df and 0.05 level,critical value χ2=		3.841
Decision rule : reject Ho if value of test statistic X2>3.841

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	Male	13.16	33.84	47
	Female	14.84	38.16	53
	total	28	72	100
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	Male	0.002	0.001	0.0027
	Female	0.002	0.001	0.0024
	total	0.0037	0.0014	0.0051
test statistic X2=		0.005

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that Exercise and Gender are dependent.