Question

3. Suppose that we want to test for the difference between two population variances. Explain which test we would use. Compare this test with tests for the difference in two population means.

Plz type answer and try to write a page

Answer 1

Answer:-

Given that:-

If we want to test for the difference between two population variances., we should use F-test for that purpose.

Suppose , we want to test

i.e., the difference between 2 population variances (say ,) is equal to .

vs   not

Under the null hypothesis,

Required test statistic 'F' is given by,

where,

which are unbiased estimates of population variances

respectively)

i.e., are independent chi-square variates with &

d.f respectively.

d.f

Now ,to test difference in two population means we use a number of tests such as Z-test,

t - tests

1) independnet t - test

2) paired t- test

as required.

So, in comparison to difference of population variances test we can say that there are 3 types of tests for the purpose of testing the difference in population means.

• If the population variances are known the population distribution are normal we can use a Z -test in that case.
• If the population variances are unknown the populations are normally distributed and independent to each other then we can use independent t - test.
• If there is a dependency or a paired relation is the two population i.e., if the population is a fivariate population in that case we use paired t- test