The director of student services at Oxnard College is interested in whether women are less likely to attend orientation than men before they begin their coursework. A random sample of freshmen at Oxnard College were asked what their gender is and whether they attended orientation. The results of the survey are shown below:
Women | Men | |
---|---|---|
Yes | 456 | 493 |
No | 204 | 197 |
What can be concluded at the αα = 0.05 level of significance?
Answer:
Given,
sample proportion p1 = x1/n1 = 456/660 = 0.6909
p2 = x2/n2 = 493/690 = 0.7145
Pooled proportion p = (x1 + x2)/(n1 + n2)
substitute values
= (456+493)/(456+493+204+197)
= 949 / 1350
= 0.7029
q = 1 - p
= 1 - 0.7029
= 0.2971
Standard error = sqrt(pq(1/n1 + 1/n2))
substitute values
= sqrt(0.7029*0.2971(1/660 + 1/690))
= 0.0248
test statistic z = (p1 - p2)/se
substitute values
= (0.6909 - 0.7145)/0.0248
= - 0.9516
P value = P(z < - 0.9516)
= 0.1706499 [since from z table]
= 0.1706
Here we observe that p value > alpha, so we fail to reject Ho.
So there is no sufficient evidence to support the claim.
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