Question

If I collect many different samples and calculate P^ for each sample, then calculate x% confidence interval for each P^, what percentage of intervals will contain P? What percentage will not contain P? (Hint: X% is the level of confidence. If this question confuse you, first consider a certain x, such as 95, and answer the question for this percent. Then think about what this means for any x)

Answer 1

If I collect many different samples and calculate for each sample, then calculate x% confidence interval for each : Percentage of intervals will contain P is given by:

x%.

Percentage of intervals will not contain P is given by:

(1 - x) %

EXPLANATION:

x% Confidence interval is a range of values that we can be x% certain contains the true proportion of the population. If we take a large number of samples and compute a x% confidence interval for each sample, then approximately x% of the confidence intervals will contain the true population proportion P.