Question

Test whether males are less likely than females to support a ballot initiative, if 24% of a random sample of 50 males plan to vote yes on the initiative and 32% of a random sample of 50 females plan to vote yes. Does this scenario represent a confidence interval or a hypothesis test?

Answer 1

the given scenario represents a hypothesis test

The hypothesis test is to test whether the proportion of males is less than the proportion of females

p1cap = X1/N1 = 12/50 = 0.24
p1cap = X2/N2 = 16/50 = 0.32
pcap = (X1 + X2)/(N1 + N2) = (12+16)/(50+50) = 0.28

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

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.24-0.32)/sqrt(0.28*(1-0.28)*(1/50 + 1/50))
z = -0.89

P-value Approach
P-value = 0.1867