Question: It is true that, when constructing a confidence interval for a population mean , we use the z distribution when sample size is 30 or

It is true that, when constructing a confidence interval for a population mean, we use the z distribution when sample size is 30 or higher, and the t distribution when it is lower than 30 . However such a rule is no longer valid when constructing confidence intervals for a population proportion. For proportions, sample sizes should be big-enough (often much larger than 30) so that both conditions (i) np>10 and (ii) n(1-p).10 are satisfied. (The Rule of Sample Proportions) The use ofthe zdistribution will then become justified when both of the above two conditions are satisfied.

In your opinion, what are the practical implication of the above two conditions? In other words, how do these conditions ensure that n is large enough for estimating a population proportion?

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