9.50 One way to evaluate the effectiveness of a teaching assistant is to examine the scores achieved by his or her students on an examination at the end of the course. Obviously, the mean score is of interest. However, the variance also contains useful information— some teachers have a style that works very well with more-able students but is unsuccessful with less-able or poorly motivated students. A professor sets a standard examination at the end of each semester for all sections of a course. The variance of the scores on this test is typically very close to 300. A new teaching assistant has a class of 30 students whose test scores had a variance of 480. Regarding these students’ test scores as a random sample from a normal population, test, against a two-sided alternative, the null hypothesis that the population variance of their scores is 300.

Given that a professor sets a standard examination at the end of each semester for all sections of a course. The variance of the scores on this test is typically very close to 300.

[tex]H_0: s^2 = 300\\H_a: s^2 \neq 300[/tex]

(Two tailed test for variance )

Sample variance =480

We can use chi square test for testing of hypothesis

Test statistic = [tex]\frac{(n-1)s^2}{\sigma^2} \\=62.4[/tex]

p value = 0.0100

Since p <0.05 our significance level, we reject H0.

The sample variance cannot be claimed as equal to 300.