Problem 2 (CLO 2, 3, 4): A study published in the AAU Journal of Business and La

Question

Problem 2 (CLO 2, 3, 4): A study published in the AAU Journal of Business and Law investigated differences in traditional and nontraditional students, where nontraditional students are defined as 25 years old or older and working. Based on the study results, we can assume the population mean and standard deviation for the GPA of nontraditional students are µ = 3.5 and ? = 0.5. Suppose a random sample of 100 nontraditional students is selected and each student's GPA is calculated. a) What is the value of ? b) What is the value of ? c) Find the interval that contains 95.44 percent of the sample means for nontraditional students d) What is the probability that the random sample of 100 nontraditional students has a mean GPA greater than 3.42?

Explanation / Answer

a) E(Xbar) = 3.5

b) sd(Xbar) = ? /sqrt(n) = 0.5/sqrt(100) = 0.05

c)

95.44 % confidence interval

z = 2

hence

(Xbar - z * sd(Xbar) , Xbar + z * sd(Xbar))

=(3.5 - 2 * 0.05 , 3.5 + 2 * 0.05 )

=(3.4 , 3.6)

d)

P(Xbar > 3.42)

=P(Z>(3.42-3.5)/0.05))

=P(Z> -1.6)

=

0.9452

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