Question

# The director of student services at Oxnard College is interested in whether women are less likely...

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 456 493 204 197

What can be concluded at the αα = 0.05 level of significance?

• The test statistic ? z t Correct =  (please show your answer to 3 decimal places.)

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.