ACT scores of a sample of UTC students are shown below. Student ACT Score A 22 B 28 C 20 D 21 E 28 F 23 G 26 a. Compute the mean and the variance. B. At 95% confidence, test to determine whether or not the variance of the ACT scores of the population of UTC students is significantly more than 8.

Solution :

a). Let  x denotes ACT scores.

ACT scores =

Mean,

Sample variance,

                                   = 11

b). To test whether or not variance of ACT scores of population (say ) of the UTC students is significantly more than 8.

Consider the hypothesis :

 vs

It is a right tailed test and α = 0.05

We have

So test statics is

   = 8.25

Since our and it falls in a acceptation region, hence we fail to reject and conclude that variance is not greater than 8 significantly.