It has been seen that the mean grade point average for students who live on camp

Question

It has been seen that the mean grade point average for students who live on campus is 2.64 with standard deviation of 0.43, while that of students who live off campus is 2.37 with standard deviation of 0.69. 6 sophomores are randomly selected from campus dormitories at a college and 12 sophomores are randomly selected from students who live off campus. The mean grade point averages of the two groups are compared.

1) The expected difference in the sample grade point average between the students who live on campus to those who live off campus is:

2) The standard deviation of the difference in the sample grade point average between the students who live on campus to those who live off campus is:

3) Assume that the grade point average distribution for both on and off campus students are approximately normal. The probability that the difference in grade point average between the students who live on campus to those who live off campus in the above sample is less than 0.31, i.e. P(x¯1?x¯2<0.31): [answer to 4 decimal places] :

Explanation / Answer

x1 (Mean GPA of Students living on Campus) = 2.64

s1 (Std Deviation of GPA of Students living on Campus) = 0.43

n1(No of Students living on Campus) = 6

x2 (Mean GPA of Students living on Campus) = 2.37

s2 (Std Deviation of GPA of Students living on Campus) = 0.69

n2(No of Students living on Campus) = 12

1)

Hence, expected difference in the sample grade point average between the students who live on campus to those who live off campus = 2.64 – 2.37 = 0.27

2)

Pooled Std Error (se) = {s12/n1 + s22/n2}1/2 = 0.2655

3)

Test Statistic:

Z = (x1-x2)/se = (0.27)/0.2655 = 1.02

Hence, (using the z-table)

P(x<Z) = 0.8461

Since, the Probability of difference of GPA is greater than 0.31

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