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 695 employed persons and 663 unemployed persons are independently and randomly selected, and that 446 of the employed persons and 305 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 6: State the null and alternative hypotheses for the test.

Step 2 of 6: Find the values of the two sample proportions, pˆ1p^1 and pˆ2p^2. Round your answers to three decimal places.

Step 3 of 6: Compute the weighted estimate of p, 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 three decimal places.

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

Answer 1

step 1:

null Hypothesis:    Ho:    p1-p2	=	0.00
alternate Hypothesis: Ha:   p1-p2	>	0.00

Step 2 of 6

p1^ =0.642

p2^ =0.460

: Step 3 of 6:

pooled prop p̂ =(x1+x2)/(n1+n2)=

0.5530

Step 4 of 6:

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =	0.0270
test stat z=(p̂1-p̂2)/Se =	6.74

Step 5 of 6:

Decision rule :                   reject Ho if test statistic z > 1.645

Step 6 of 6:

reject the null hypothesis