Question 1088021
<font color="black" face="times" size="3">Define the following 


p1 = population proportion of males that live on campus
x1 = number of successes for the males = number of males that live on campus
n1 = sample size of the males
phat1 = sample proportion of males that live on campus
.......
p2 = population proportion of females that live on campus
x2 = number of successes for the females = number of females that live on campus
n2 = sample size of the females
phat2 = sample proportion of females that live on campus


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Based on what we're given, we can determine that...


p1 = unknown
x1 = 24
n1 = 40
phat1 = x1/n1 = 24/40 = 0.6
.......
p2 = unknown
x2 = 43
n2 = 55
phat2 = x2/n2 = 0.7818 (approximate; accurate to 4 decimal places)


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Null Hypothesis:
H0: p1 = p2 (population proportions for male and female groups are the same)


Alternative Hypothesis
H1: p1 =/= p2 (population proportions for male and female groups are different)


This is a two tailed test. We will use a two proportion Z test. 
We will reject H0 if the test statistic is in the critical region, which is outside the interval -1.96 < Z < 1.96


When the significance level is alpha = 0.05, the noncritical region is the interval -1.96 < Z < 1.96


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The pooled phat is calculated below


phat = (x1+x2)/(n1+n2)
phat = (24+43)/(40+55)
phat = 67/95
phat = 0.7053 (approximate; accurate to 4 decimal places)


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Standard Error (SE)


SE = sqrt(phat*(1-phat)*(1/n1+1/n2))
SE = sqrt(0.7053*(1-0.7053)*(1/40+1/55))
SE = 0.0947 (approximate; accurate to 4 decimal places)


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Z test statistic


Z = (phat1-phat2)/(SE)
Z = (0.6-0.7818)/(0.0947)
Z = -0.1818/0.0947
Z = -1.9197 
Z = -1.92 (approximate; accurate to 2 decimal places)


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The Z test value is Z = -1.92 which is inside the noncritical region (aka the non-rejection region). 
The value Z = -1.92 is in the interval -1.96 < Z < 1.96



So we fail to reject the null. We have to accept that the population proportions p1 and p2 are equal. 


There is NOT enough sufficient evidence to support the claim that a difference exists between the proportions of male and female students who live on campus.


<font color=red>Answer is choice D</font>


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