In constructing 95 confidence intervals for means over the l

In constructing 95% confidence intervals for means, over the long run, about what percentage of the time would each of the following happen?

(a) The distance between the sample mean and the population mean is less than the margin of error

% of the time

(b) The distance between the sample mean and the population mean is more than the margin of error

% of the time

Solution

By definition, the confidence level is the percentage of times where the distance from the sample mean and population mean is less than the margin of error. Hence,

a) 95% of the time [ANSWER]

b) 100% - 95% = 5% [ANSWER]