Economists theorize that the recent recession has affected men more than women because men are typically...

Economists theorize that the recent recession has affected men more than women because men are typically employed in industries that have been hit hardest by the recession. Women, on the other hand, are typically employed in services which are considered more recession resistant. A sample of

175175

men and a sample of

150150

women were drawn. In those samples,

1919

men were unemployed, and

1111

of the women were unemployed. Complete parts a and b below.

a. Perform a hypothesis test using

alphaαequals=0.05

to determine if the unemployment rate for men is higher than the rate for women.

Let population 1 be men and population 2 be women. What are the correct null and alternative hypotheses?

What is the test statistic?

zpequals=nothing

(

Solutions

Expert Solution

Given that,
sample one, x1 =19, n1 =175, p1= x1/n1=0.109
sample two, x2 =11, n2 =150, p2= x2/n2=0.073
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.109-0.073)/sqrt((0.092*0.908(1/175+1/150))
zo =1.094
| zo | =1.094
critical value
the value of |z α| at los 0.05% is 1.645
we got |zo| =1.094 & | z α | =1.645
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.0941 ) = 0.13696
hence value of p0.05 < 0.13696,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 1.094
critical value: 1.645
decision: do not reject Ho
p-value: 0.13696
we do not have enough evidence to support the claim that if the unemployment rate for men is higher than the rate for women.
Let population 1 be men and population 2 be women.

orchestra answered 1 year ago

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