Chapter 19 Confidence Intervals for Proportions

Confidence interval: A level C confidence interval for a model parameter is an interval of values usually of the form Estimate ± margin of error found from data in such a way that C% of all random samples will yield intervals that capture the true parameter value.

One-proportion z-interval: A confidence interval for the true value of a proportion. The confidence interval is where Z* is a critical value from the Standard Normal model corresponding to the specified confidence level.

Margin of error: In a confidence interval, the extent of the interval on either side of the observed statistic value is called the margin of error. A margin of error is typically the product of a critical value from the sampling distribution and a standard error from the data. A small margin of error corresponds to a confidence interval that pins down the parameter precisely. A large margin of error corresponds ato a confidence interval gives relatively little information against the estimated parameter.

Critical value: The number of standard errors to move away from the mean of the sampling distribution to correspond to the specified level of confidence. The critical value is usually found form a table or with technology.

Assumptions: Every model depends on assumptions. Although we may be able to think about whether an assumption is plausible, it remains something that we assume and cannot verify.

Conditions: Although we cannot verify assumptions, often there are conditions about the data that we can check to see whether an assumption is at least reasonable.