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 700 employed persons and 300 unemployed persons are independently and randomly selected and that 500 of the employed persons and 200 of the unemployed persons have registered to vote. Can we conclude that the percentage of the employed workers (p1), who have registered to vote, exceeds the percentage of unemployed workers (p2), who have registered to vote

Answer 1

Yes. We can conclude that the percentage of the employed workers (p1), who have registered to vote, exceeds the percentage of unemployed workers (p2), who have registered to vote.

Explanation:

Number of employed persons in the sample = 700

Number of unemployed person in the sample = 300

Number of employed persons who have registered to vote (p1) = 500

Number of unemployed persons who have registered to vote (p2) = 200

Proportion of registered voters who are employed = 500/700 = 71.4%

Proportion of registered voters who are unemployed = 200/700 = 28.6%

This implies that the percentage of registered voters who are employed is more than the percentage of registered voters who are employed. 71.4% (500/700) of the employed registered to vote as against 66.7% (200/300) of the unemployed who registered to vote.

We can conclude that of the 700 registered voters in the sample, 71.4% (500/700) are employed while 28.6% (200/700) are unemployed.

Therefore, the percentage of the employed workers (p1), who have registered to vote, exceeds the percentage of unemployed workers (p2), who have registered to vote.