Determine required sample size with unknown standard deviation

Question

An exercise : A quality control engineer gets 1000 items. How big a sample will he require to say that the he is 95% confident that the sample represents the population?? Is this possible to answer without knowing anything else?? All examples that I have seen so far work with either certain values and/or known standard deviation and certain samples.

My question basically is: is Cochran's formula enough / suitable if I want to determine minimum sample size to examine in order to get confidence about the whole population? Lets say I have a batch of 1000 phones. I cannot test all of them but I need to test enough of them to be somehow confident that the whole population has the same property (e.g. simply is working). This Cochran's formula seems to be exactly what I need but I am not sure.

Can Cochran's formula be used here?

What does "the sample represents the population" mean? (where it must be defined in a way that it makes sense to speak of confidence in the statistical sense). I really don't know what you're asking. — Glen_b, Jan 05 '16 at 10:51
See here for how to merge your accounts. And see How to calculate a sample size for validating correct/incorrectness of records in a data table? for one way of dealing with the 'phone problem described in your edit: take a random sample of 'phones from the batch & consider the count of those not working as a hypergeometric random variable. — Scortchi - Reinstate Monica, Jan 05 '16 at 13:18

score 0 · Answer 1 · answered Jan 05 '16 at 07:18

You have not defined the question sufficiently. If in this particular circumstance the question revolves around a proportion or a rate with an arguably Poisson distribution, then you are in luck, since the variance and therefore the standard deviation are determined by the observed value (at least if we are reasoning from a frequentist perspective. Binomial or GLM models with Poisson errors would be useful in those particular instances. On the other hand if you are estimating a continuous quality and wan a mean, then you have an additional parameter to estimate.

Please clarify the question to support further refinement.

Determine required sample size with unknown standard deviation

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