At one university, all students taking Statistics 101 take the same statistics f

Question

At one university, all students taking Statistics 101 take the same statistics final. Historically, the scores on this 100-point final are normally distributed, and has a population mean of 83.4 points and a population variance of 26.8 points. This year, the university has implemented a new curriculum and the professors believe that this new curriculum has resulted in a reduction in the variability of the final scores. Researchers took a random sample of 35 students and found the sample variance to be 23.1 points. Is there evidence at the = 0.05 level of significance to support the notion that the new curriculum is associated with lower score variability?

Explanation / Answer

step 1:

ho: sigma^2 = 26.8

h1: sigma^2 < 26.8

step 2:

alpha = 0.05

step 3:

chisq = (n-1)*s^2/sigma^2

chisq = 34*(23.1/26.8) = 39.44

step 4:

chisq(a,n-1) =21.6642

step 5:

since chisq > chisq(a,n-1) i fail to reject ho at 5% level of signifcance and conclude that sigma^2 = 26.8.

that is there is no evidence to support the notion that the new curriculum is associated with lower score variability

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