https://onlinecourses.science.psu.edu/stat414/node/167(adsbygoogle = window.adsbygoogle || []).push({});

in the link they prove variance of samples. It is a bit long to write it all here so I hope one can read link. Main problem for me i will write here. It starts with:

[tex]Var(\frac{X_1+X_2...X_n}{n})[/tex]

they write n here because it is n samples to get mean of samples. But later in the text they say :

If the instructor had taken larger samples of students, she would have seen less variability in the samples she was obtaining. That is a good thing , but of course, in general, the costs of research studies no doubt increase as the sample size n increases

it seems they are refering to n as number of elements in each sample but from proof it seems to be number of samples. I dont get this. And they also assume that variance is the same for all samples (the second final step) but the example refered to about the teacher which is on the page before in the link have differnt variances.

From examples in my text book it also seems that n is number of tests in a sample not the number of samples which i thought would make sense from this proof

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# Variances of samples

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