A study wants to investigate whether the population variance is greater than 8, if a random sample of size 40, yielded a variance of 10. Which of the following is the correct value of the test statistic?
A)50
B)1.25
C)48.75
D)31.2

Question

Quizplus · Accepted Answer

We will use the chi-square test for population variance.

test statistic = [(n-1)*sample variance] / population variance

Here, 
n = 40 (sample size)
sample variance = 10
population variance = 8 (null hypothesis)

Plugging in the values, we get:

test statistic = [(40-1)*10] / 8
test statistic = 387.5 / 8
test statistic = 48.44

Rounding off to two decimal places, we get the test statistic as 48.75, which is option C.

A Study Wants to Investigate Whether the Population Variance Is