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 680 employed persons and 686 unemployed persons are independently and randomly selected, and that 378 of the employed persons and 273 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2p2 ), who have registered to vote? Use a significance level of α=0.05 for the test.

Step 1 of 6 :  State the null and alternative hypotheses for the test.

Step 2 of 6: Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 3 of 6: Compute the weighted estimate of p, p‾. Round your answer to three decimal places.

Step 4 of 6: Compute the value of the test statistic. Round your answer to two decimal places.

Step 5 of 6: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 6 of 6: 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 = 378/680 = 0.556
p2cap = X2/N2 = 273/686 = 0.398

3)

pcap = (X1 + X2)/(N1 + N2) = (378+273)/(680+686) = 0.477

4)

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.556-0.398)/sqrt(0.477*(1-0.477)*(1/680 + 1/686))
z = 5.85

5)
Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

6)

reject the null hypothesis.