Question

Suppose that the student body in a large university have normally distributed GPAs with a mean of μ=2.91 and standard deviation σ=0.38. You randomly select a sample of n=29 students. The probability is 0.95 (with the complement split evenly between the tails) that the standard deviation of your sample will be between what two numbers? Round your answers to four decimal places.

________ ≤ s ≤ ________

Answer 1

chi square value for lower bound = 44.461
chi square value for upper bound = 15.308

(n-1)s2 Xi α/2 χα/2

lower bound = sqrt(28*0.38^2/44.461) = 0.3016
upper bound = sqrt(28*0.38^2/15.308) = 0.5139

0.3016 < s < 0.5139