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?

1. What is the alternative hypothesis?

2. What is the estimated proportion of unemployed people who are registered to vote; that is, what is p-hat 2?

3.  If the significance level is 0.1, what is the critical z-value?

4. Assume that the calculated test statistic is 2.02 (use this value even if you found another value in your calculations). Then, what is the conclusion to the hypothesis test? Use the critical z-value from Question 3.

Answer 1

Given that,
sample one, x1 =500, n1 =700, p1= x1/n1=0.714
sample two, x2 =200, n2 =300, p2= x2/n2=0.667
finding a p^ value for proportion p^=(x1 + x2 ) / (n1+n2)
p^=0.7
q^ Value For Proportion= 1-p^=0.3
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, α = 0.1
from standard normal table,right tailed z α/2 =1.28
since our test is right-tailed
reject Ho, if zo > 1.28
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.714-0.667)/sqrt((0.7*0.3(1/700+1/300))
zo =1.506
| zo | =1.506
critical value
the value of |z α| at los 0.1% is 1.28
we got |zo| =1.506 & | z α | =1.28
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: right tail - Ha : ( p > 1.5058 ) = 0.06605
hence value of p0.1 > 0.06605,here we reject Ho
ANSWERS
---------------
1.
null, Ho: p1 = p2
alternate, H1: p1 > p2
2.
the estimated proportion of unemployed people who are registered to vote
sample two, x2 =200, n2 =300, p2= x2/n2=0.667
3.
critical value: 1.28
4.
test statistic: 1.506
decision: reject Ho
p-value: 0.06605
we have enough evidence to support the claim 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