Sampling Distribution & Confidence Intervals of Proportions

point estimator

Statistic that provides an estimate of a population parameter.

point estimate

Specific value of a point estimator from a sample.

confidence interval

Gives an interval of plausible values for a parameter. The interval is calculated from sample data and has the form point estimate ± margin of error or, alternatively, statistic ± (critical value) * (standard error of statistic)

confidence level C

Overall success rate of the method used to calculate the confidence interval. In C% of all possible samples, the method would yield an interval that captures the true parameter value when the conditions for inference are met.

margin of error

Describes how far, at most, we expect the estimate to vary from the true population value. That is, the difference between the point estimate and the true parameter value will be less than the margin of error in C% of all samples, where C is the confidence level.

critical value

Multiplier that makes a confidence interval wide enough to have the stated capture rate. The critical value depends on both the confidence level C and the sampling distribution of the statistic.

standard error

When the standard deviation of a statistic is estimated from data, the result is the standard error of the statistic. The standard error estimates how far the value of the statistic typically varies from the value it is trying to estimate.

statistic

Number that describes some characteristic of a sample.

parameter

A number that describes some characteristic of a population.

sampling variability

The fact that different random samples of the same size from the same population produce different estimates.

sampling distribution

The distribution of values taken by a statistic in all possible samples of the same size from the same population.

unbiased estimator

A statistic used for estimating a parameter is unbiased if the mean of its sampling distribution is equal to the value of the parameter being estimated.

sampling distribution of a sample proportion (p-hat)

The distribution of values taken by the sample proportion p in all possible samples of the same size from the same population.