In comparing the academic performance of college students who are affiliated wit
ID: 3340645 • Letter: I
Question
In comparing the academic performance of college students who are affiliated with fraternities and those male students who are unaffiliated, a random sample of students was drawn from each of the two populations on a university campus. Summary statistics on the student GPAs are given below.
n Sample mean Sample standard deviation
Fraternity 645 2.90 0.47
Unaffiliated 450 2.88 0.42
Test, at the 5% level of significance, whether the data provide sufficient evidence to conclude that there is a difference in average GPA between the population of fraternity students and the population of unaffiliated male students on this university campus.
Explanation / Answer
P = 0.4696
Since P> 0.05, the data does not provide sufficient evidence to conclude that there is a difference in average GPA between the population of fraternity students and the population of unaffiliated male students on this university campus.
s = sqrt( (644 * 0.47^2 + 449* 0.42^2)/(645+450-2))
se = s * sqrt( 1/645+1/450) = 0.028
t = difference of means /se = -0.020/0.028= -0.723
p-value for t= -0.723 is 0.4696
Difference -0.020 Standard error 0.028 95% CI -0.0742 to 0.0342 t-statistic -0.723 DF 1093 Significance levelP = 0.4696
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