A 90% confidence interval around the variance was calculated. For n=27, ?

Question

the confidence interval was 35.0-88.4. Give the variance of the sample.

Answer 1

For 90% confidence interval, the range is:

[(n-1)(S^2)]/Chi-sq0.05(n-1) ~ [(n-1)(S^2)]/Chi-sq0.95(n-1)

S is the standard deviation, hence, variance is S^2

now n=27, n-1 = 26

lookup Chi-sq values from a table or by using Excel:

Chi-sq0.05(26) = 38.885

Chi-sq0.95(26) = 15.379

plug those number into the range expression:

26(S^2)/38.885 ~ 26(S^2)/15.379

0.6686(S^2) ~ 1.6906(S^2)  =  35.0 ~ 88.4

0.6686(S^2) = 35.0  ----->  S^2 = 52.3

1.6906(S^2) = 88.4  ----->  S^2 = 52.3

they have the same value ----> OK

variance = S^2 = 52.3