Question

Test scores on a course’s final test have historically followed a X ~ NORM( 77, 8 ) distribution.  For the latest test, S=12 with n=30.  Is this consistent with the variability of the historical distribution? Show supporting calculations and explanation

Test scores on a course's final exam have historically followed a X ~ NORM( 77, 8 ) distribution. For the latest final exam, S=12 with n=30. Is this consistent with the variability of the historical distribution? Show supporting calculations and explanation

Answer 1

As we are testing here whether there is a change in the variability of the distribution, therefore this is a test for a change in standard deviation, therefore the chi square test statistic here is computed as:

$\chi^2 = \frac{(n - 1)s^2}{\sigma_0^2} = \frac{(30-1)12^2}{8^2} = 65.25$

For n - 1 = 29 degrees of freedom, the p-value here is computed from the chi square distribution tables as:

p = P(X29 > 65.25) = 0.0001

As the p-value here is very very low, therefore the test is significant here and we have sufficient evidence here that the new variability is not consistent with the original one.