Question

A candidate for political office wants to determine if there is a difference in his popularity between men and women. To test the claim of this difference, he conducts a survey of voters. The sample contains 250 men and 250 women, of which 44% of the men and 52% of the women favor his candidacy. Do these values indicate a difference in popularity? Use a 0.01 significance level.

Which statement properly summarizes the results?

		The sample evidence indicates a significant difference in the candidate's popularity.
		The sample evidence does not indicate a significant difference in the candidate's popularity.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

pcap = (X1 + X2)/(N1 + N2) = (110+130)/(250+250) = 0.48

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.44-0.52)/sqrt(0.48*(1-0.48)*(1/250 + 1/250))
z = -1.7903

P-value Approach
P-value = 0.0734
As P-value >= 0.05, fail to reject null hypothesis.

The sample evidence does not indicate a significant difference in the candidate's popularity