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 665 employed persons and 652 unemployed persons are independently and randomly selected, and that 379 of the employed persons and 261 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, 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 two decimal places.

Reject H0 if (z, IzI) (<,>), _____

Step 6 of 6: Make the decision for the hypothesis test. (Reject or Fail to Reject Null Hypothesis)

Answer 1

1) Hypothesis

p₁: proportion where employed and registered for vote

p₂: proportion where unemployed and registered for vote

Difference: p₁ - p₂

H₀ : p1 = p2

H₁ : p1 > p2

alpha = 0.01

2)

Descriptive Statistics

Sample	N	Event	Sample p
Employed	665	379	0.570
Unemployed	652	261	0.400

3)

weighted estimate of p = = (379+261)(665 + 652) = 0.486

4) test statistic Z = = 6.172

5) decision rule if test stat Z is greater than critical value 2.33 then reject null hypothesis otherwise fail to reject.

6) Since Z > Z_0.01 we reject null hypothesis. there is a significant 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