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 608 employed persons and 719 unemployed persons are independently and randomly selected, and that 318 of the employed persons and 269 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, 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 two decimal places.

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

Answer 1

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 608 employed persons and 719 unemployed persons are independently and randomly selected, and that 318 of the employed persons and 269 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.

Upper tail 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.

p1= 318/608 =0.523

p2=269/719 = 0.374

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

p =(318+269)/(608+719) = 0.442

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

=5.44

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

Table value of z at 0.01 level = 2.33

Rejection Region: Reject Ho if z > 2.33

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

Since calculated z= 5.44 > 2.33 critical value, Ho is rejected.

There is enough 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.

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.01
Group 1
Number of Items of Interest	318
Sample Size	608
Group 2
Number of Items of Interest	269
Sample Size	719
Intermediate Calculations
Group 1 Proportion	0.5230
Group 2 Proportion	0.3741
Difference in Two Proportions	0.1489
Average Proportion	0.4424
Z Test Statistic	5.4412
Upper-Tail Test
Upper Critical Value	2.3263
p-Value	0.0000
Reject the null hypothesis