Question

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

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.

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

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