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Edexcel S4 Statistics - Help with t-distribution

I'm currently studying the t-distribution in S4 Statistics and I have run into a bit of a problem. To start, I am aware of the meaning of the t-distribution and how it arises when the variance of a normal population is estimated and the sample size is small.

What stumps is me is how in the Edexcel Maths book for S4, in some cases they will use the sample variance as the estimate instead of the best unbiased estimator of population variance. Why is this done? Or, more importantly when it comes to answering Statistics problems, how am I supposed to know when to use either one?

P.S I have checked thoroughly - they are indeed using sample variance in some places and the unbiased estimate of population variance in others.

Any help would be greatly appreciated,
VannR

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