Question

If you have taken 1000 samples and generated a 95% confidence interval for each sample (therefore you have 1000 different 95% confidence intervals) for a population mean u, roughly how many of the intervals would you expect to actually contain u?

Answer 1

A 95% confidence interval means the mthod used to construct the interval will produce intervals containing mu in about 95% of the intervals constructed.

This means that if 95% CI method was used in 100 different samples,we would expect about that about 95 of the intervals contain true mean ,and about 5 intervals would not contain mu

so

0.95*1000=950

In 950 intervals we would expect to contain actually mean

and 50 intervals would not expect to contain actual mean

950