Confidence intervals for proportions

Learning objectives

Identify a one-sample z-interval as the procedure for estimating a population proportion, define the parameter in context, and check the random, 10% and large counts conditions using the observed numbers of successes and failures

Calculate the standard error √(p̂(1 − p̂)/n), the margin of error and the confidence interval p̂ ± z* × standard error for a population proportion

Interpret a confidence interval in context, and interpret the confidence level as the long-run percentage of intervals that capture the parameter, explaining why no probability attaches to one computed interval

Justify a claim about a population proportion from a confidence interval, and describe how the confidence level and the sample size change the critical value, the margin of error and the width of the interval

Determine the sample size needed for a stated margin of error, using 0.5 for the proportion when no estimate is available

Check the conditions for a two-sample z-interval for a difference between two population proportions, calculate and interpret the interval, and justify a claim from whether it contains zero