Question

A study of 150 randomly selected workers from Dallas County and 180 randomly selected workers from Harris County shows that 25 of the Dallas county workers and 35 of the Harris county workers have filed an unemployment claim. At α = 0.05, can you support the claim that the proportion of workers who have filed an unemployment claim is higher in Harris County? Please show work.

Answer 1

p1cap = X1/N1 = 25/150 = 0.1667
p2cap = X2/N2 = 35/180 = 0.1944
pcap = (X1 + X2)/(N1 + N2) = (25+35)/(150+180) = 0.1818

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 = (0.1667-0.1944)/sqrt(0.1818*(1-0.1818)*(1/150 + 1/180))
z = -0.65

P-value Approach
P-value = 0.2578
As P-value >= 0.05, fail to reject null hypothesis.