Question

How do you know when to check normality or indepencence when constructing confidence intervals for proportions and means?

Answer 1

The normal condition:

While constructing confidence intervals for means, the sampling distribution of mean should be approximately normal. And a sample distribution can be approximate to its population if the sample size is sufficiently large such that

While constructing confidence intervals for proportions, the necessary condition for a sample distribution of proportion to be approximately normal is, . Where 'np' is the expected number of success in a sample which should be greater than equal to 10.

The independence condition:

While constructing confidence intervals for means, the standard error in the formula requires independence of the observations in the sample. And this condition holds if the sample size is 10% or less of the population (10% rule) when sampling is being done without replacement.

Similarly while constructing confidence intervals for proportions, the 10% rule condition should be follow.