Question

Suppose that a random sample of

100

men between the ages of 25 and 54 was selected and it was found that

80

were currently working. A similar sample of

100

women was selected and

70

were working. Complete parts a and b below.

a. Using

α=0.05​,

can it be concluded that the proportion of men in this age group who are working differs from the proportion of women who are​ working?

Determine the null and alternative hypotheses. Choose the correct answer below.

A.

H0​:

pM=pW

H1​:

pM≠pWYour answer is correct.

B.

H0​:

pM<pW

H1​:

pM>pW

C.

H0​:

pM=pW

H1​:

pM>pW

D.

H0​:

pM≠pW

H1​:

pM=pW

E.

H0​:

pM=pW

H1​:

pM<pW

F.

H0​:

pM>pW

H1​:

pM<pW

What is the test​ statistic?

χ2=nothing

​(Round to two decimal places as​ needed.)

Answer 1

Ans. Let proportion of men currently working, pm = 80/100 = 0.8

and proportion of women currently working, pw = 70/100 = 0.7

Sample size, n = 100

Average proportion, p = (80+70)/(100+100) = 0.75

pW and pM are corresponding population proportions.

Hypothesis,

H0​: pM=pW, against

H1​: pM≠pW (two tailed test)

=> z statistic = [pm-pw]/[(p(1-p)*(2/n)]^0.5 = 1.6329

At 5% level of significance, z critical = 1.96

Thus, zstatistic < zcritical, so, we fail to reject the null hypothesis.

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