i pose the following question ...
let's say that you do take a sample (decent size) and find that in a simple 1 sample t test ... are NOT able to reject the null hypothesis ...
does this mean that the SAMPLE was randomly drawn from the population??? or correctly representative OF that population?
perhaps for the MEAN ... but, what about for other things?
showing that the sample mean does not allow you to reject the null is NOT sufficient evidence to draw the conclusion that the sample is representative
the only "proof" that i know of is THE method of sampling used ... and even there ... one sample drawn at random is no assurance (as another poster mentioned) that your sample is representative ... only that IF you repeated this process over and over ... OVERALL your samples are ...
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