In an American Economic Review Dec 2008 study of college dro

In an American Economic Review (Dec. 2008) study of college dropouts, one factor thought to influence the college dropout decision was expected GPA for a student who studied 3 hours per day. In a representative sample of 307 college students who studied 3 hours per day, the mean GPA was xbar = 3.11 and the standard deviation was s = .66. Of interest is , the true mean GPA of all college students who study 3 hours per day.

a. give an interval that will contain most (at least 75% to apporximately 95%) of the 307 GPAs.

b. if you observe a GPA of 1.25, is it likely that this college student studied 3 hours per day? Explain

Solution

a)

By chebyshev\'s theorem and empirical rule, this refers to within 2 standard deviations from the mean.

Thus, we have the interval

3.11 - 2(0.66) < x < 3.11 + 2(0.66)

or

1.79 < x < 4.43 [ANSWER]

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b)

Yes, as it is outside the interval given in A.