Question

Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test.

n1 = 50 x1 = 8 n2 = 50 x2 = 7

Answer 1

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

p1cap = X1/N1 = 8/50 = 0.16
p2cap = X2/N2 = 7/50 = 0.14
pcap = (X1 + X2)/(N1 + N2) = (8+7)/(50+50) = 0.15

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.16-0.14)/sqrt(0.15*(1-0.15)*(1/50 + 1/50))
z = 0.28

P-value Approach
P-value = 0.7795

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