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About the part of two independent samples test in 2 sample hypothesis testing, why need to...

About the part of two independent samples test in 2 sample hypothesis testing, why need to assume sigma1 = sigma2 (s.d) when using t test? thx~
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Answer #1

You necessarily don't have to.

We assume sigma1 = sigma2 if one sigma is less than twice of the other.

For example:

If sigma1 = 2, sigma2 = 3.5

Since sigma2 < 4, we can assume that sigma1 = sigma2.

For example:

If sigma1 = 2, sigma2 = 4.5

Since sigma2 > 4, we cannot assume that sigma1 = sigma2.

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