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 366 employed persons and 422 unemployed persons are independently and randomly selected, and that 202 of the employed persons and 186 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 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places.

Step 4 of 4: Make the decision for the hypothesis test.

Answer 1

1)

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

2)

p1cap = X1/N1 = 202/366 = 0.5519
p1cap = X2/N2 = 186/422 = 0.4408
pcap = (X1 + X2)/(N1 + N2) = (202+186)/(366+422) = 0.4924

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5519-0.4408)/sqrt(0.4924*(1-0.4924)*(1/366 + 1/422))
z = 3.11

3)

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

4)

Reject the null hypothesis