The Wall Street ournal recently ran an article 17 years ago indicating differenc

Question

The Wall Street ournal recently ran an article 17 years ago indicating differences in perception of sexual harassment on the job between men and women. The artcle claimed than women perceived the problem to be much more prevalent than did the men. One question asked to 200 men and 300 women was "Do you think sexual harassment is a major problem in the American workplace?" 24% of men and 62% of women responded "Yes." Based on this data, can it be shown that women perceive the problem to be more prevalent than men, at the 1% level of significance.
Sample Size Proportion Responding "Yes"

Men(1) 200 .24

Women (2) 300 .62

State the hypotheses:
a) Ho: u1-u2 = 0 Ha: u1-u2 does not equal 0
b) Ho: p1-p2 = 0 Ha: p1-p2 does not equal 0
c) Ho: p1-p2 >=0 Ha: p1-p2 <0
d) Ho: u1-u2 >=0 Ha: u1-u2 <0

Calculate the appropriate test statistic:

Give the rejection region:
a) reject Ho if z<-2.33
b) reject Ho if t<-2.575
c) reject Ho if z>2.33
d) reject Ho if z<-2.575 or z>2.575

State the decision and conclusion:
a) Reject Ho because test statistic falls in the rejection region. Conclude the data does not provide sufficient evidence to support that women perceive the problem to be more prevalent than men, at a 1% level of significance.
b) Do not reject Ho because test statistic doesn't fall in the rejection region. Conclude the data doesn't provide sufficient evidenc to support that women perceive the problem to be more prevalent than mem, at the 1% level of significance.
c) Do not reject Ho because test stat. doesn't fall in the rejection region. Conclude the data provides suficient evidence to support that women perceive the problem to be more prevalent than men, at the 1% level of significance.
d) Reject Ho because test statistic falls in the rejection region. Conclude the data provides sufficient evidence to support that women perceive the problem to be more prevalent than men, at the 1% level of significance.

Explanation / Answer

H0: p1-p2>0 and HA: p1-p2<0 (left tail test)

n1= 200 and n2= 300

P(hat)= n1p1+n2p2/n1+n2= 200*0.24+300*0.62/200+300= 234/500= 0.468

Q(hat)= 1-0.468= 0.532

Under NULL HYPOTHESIS H0, test Statistic is

Z= p1-p2/ Sqrt ( P(hat)*Q(hat) *(1/n1+1/n2))

Z= 0.24-0.62/sqrt (0.468*0.532*(1/200+1/300))

Z= -0.38/sqrt(0.468*0.532(0.005+0.003)

Z= -0.38/0.0446

Z= -8.52

Critical value of Z at 0.01 level of Significance for left tailed test= -2.575

Reject H0 if Z <-2.575

Conclusion; Reject Ho because test statistic falls in the rejection region. Conclude the data provides sufficient evidence to support that women perceive the problem to be more prevalent than men, at the 1% level of significance.

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