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 418 employed persons and 413 unemployed persons are independently and randomly selected, and that 251 of the employed persons and 183 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=0.01 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, p^1 and p^2. 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 H0H0. Round the numerical portion of your answer to two decimal places.

Step 6 of 6: Make the decision for the hypothesis test.

Answer 1

Solution:

Given

n1= 418 sample size of employed persons

n2= 413 sample size of unemployed persons

X1= 251 employed persons have registered to vote

X2= 183 unemployed persons have registered to vote

. Level of significance

Step 1) To test the hypothesis

. Vs.   

Step 2) To find sample proportion

. Sample proportion of employed persons who have registered to vote.

. Sample proportion of unemployed persons who have registered to vote

Step 3) To find weighted estimate of p is

weighted estimate

Step 4 ) Test statistic

Z = 4.5303185

Test statistic Z = 4.53

Step 5) Decision rule : The rejection region of the test is

The Z critical value at is

from Z table

Reject Ho

Step 6 ) Conclusion : Reject Ho, there is sufficient evidence to 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.