Question

In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 30 scores from all of the students who took the test. She sees that the mean score is 147 with a standard deviation of 38.7896. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 26. Is there evidence that the standard deviation of test scores has increased at the α=0.01 level? Assume the population is normally distributed.

1)Null Hypothesis and alternative (4 decimal places)

2) Critical Value

3) T-test

4)reject or fail to reject

Answer 1

a)

H0 : sigma = 26
HA: sigma > 26

b)

Critical value = 49.5879

c)

Chi^2 = (n-1)s^2/sigma^2
= ((30 - 1) *38.7896^2)/26^2
= 64.5479

d)

Reject H0