Question

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

It has been seen that the mean grade point average for students who live on campus is 2.73 with standard deviation of 0.44, while that of students who live off campus is 2.48 with standard deviation of 0.67. 12 sophomores are randomly selected from campus dormitories at a college and 20 sophomores are randomly selected from students who live off campus. The mean grade point averages of the two groups are compared.

a)The expected difference in the sample grade point average between the students who live on campus to those who live off campus is: [answer to 2 decimal places]

b)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: [answer to 4 decimal places]

c)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 0.37, i.e. P([?(x)]1?[?(x)]2 < 0.37): [answer to 4 decimal places]

Math   Statistics-And-Probability   
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Answer #1

Let X is a random avriable shows the grade point average for students who live on campus and Y is a random variable shows the grade point average for students who live off campus. Here we have

(a)

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

(b)

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:

(c)

The z-score for is

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 0.37, i.e. P([?(x)]1?[?(x)]2 < 0.37):

P(z < 0.61) = 0.7291

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