Question

The U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is registered to vote. Suppose that 400 employed persons and 487 unemployed persons are independently and randomly selected, and that 221 of the employed persons and 211 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2 ), who have registered to vote? Use a significance level of α=0.05 for the test.

Step 3 of 4 : Give the value of the test statistic. Round your answers to three decimal places.

Answer 1

p1cap = X1/N1 = 221/400 = 0.553
p1cap = X2/N2 = 211/487 = 0.433
pcap = (X1 + X2)/(N1 + N2) = (221+211)/(400+487) = 0.487

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 = (0.553-0.433)/sqrt(0.487*(1-0.487)*(1/400 + 1/487))
z = 3.558

P-value Approach
P-value = 0.0002
As P-value < 0.05, reject the null hypothesis.