Question

Academic staff members at a college were cross-classified according to gender and political affiliation. The two-way table below shows the results.

	Democrat	Republican	R total
Male	39	19
Female	85	26
C total			169

Calculate the marginal counts (row and column totals) in the table. Then, conduct a test to determine whether gender and political affiliation are independent at the significance level of 0.1.

(a) State the null and alternative hypotheses.

H0:H0: Gender and political affiliation  select are are not  independent.

Ha:Ha: Gender and political affiliation  select are are not  independent.

(b) Calculate the expected counts. (Round to 3 decimal places.)

	Democrat	Republican
Male
Female

(c) Calculate the test statistic.

(Round to 3 decimal places.)

(d) Approximate the p-value.

select p-value < 0.01 0.01 < p-value < 0.05 0.05 < p-value < 0.10 p-value > 0.10  

(e) State the decision.

select Reject Fail to reject  the null hypothesis.

Answer 1

a)
H0: Gender and political affiliation are independent.

Ha: Gender and political affiliation are not independent.

b)

Observed
	Democrat	Republican	total
Male	39	19	58
Female	85	26	111
Total	124	45	169

Expected count = sum(rowi)*sum(coli)/total

for example, expected count for democrat and male = 124*58/169 = 42.56

Expected
	Democrat	Republican
Male	42.56	15.44
Female	81.44	29.56

c)

Test statistic, chi-square = sum((Oi - Ei)^2/Ei) = 1.699

d)

p-value > 0.10

e)

Fail to reject H0