Question

How could one analyse a possible difference between two population standard deviations using the notion of confidence intervals. What specif- ically should one be looking for with respect to the test intervals?

Answer 1

when we construct confidence intervals for difference between population standard deviations.

Then we observe the confidence interval

1) if confidence interval contain 0 (e.g. (-2,1)), then we conclude that the no difference between population standard deviations.

2) if confidence interval does not contain 0 (e.g. (1,5) or (-4,-2), then we conclude that the their is difference between population standard deviations.

a) if confidence interval does not contain 0 and contain positive value (e.g. (1,5) ), then we can conclude that standard deviations for   population 1 is greater than that of for population 2.

b) if confidence interval does not contain 0 and contain negative value (e.g. (-1,-5) ), then we can conclude that standard deviations for   population 1 is less than that of for population 2.