Question

A poilitical surevy was conducted where 850 participants responded to the questions (1) Political Affilation and (2) Do you think the federal goverment should supply free contraceptives to adult females. Of those 850, 662 identified them selves as either democrats or republicans. Those results are tabulated below. Is there evidence to suggest Democrats are more in favor of free contraceptives for women than republicans? Complete your analysis using an odds ratio. In Favor of Free Contraceptives Democrat Republican Yes No 206 109 142 205

Answer 1

p1cap = X1/N1 = 206/315 = 0.654
p1cap = X2/N2 = 142/347 = 0.4092
pcap = (X1 + X2)/(N1 + N2) = (206+142)/(315+347) = 0.5257

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

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.654-0.4092)/sqrt(0.5257*(1-0.5257)*(1/315 + 1/347))
z = 6.3

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

There is significant evidence to conclude that the Democrats are more in favor