Starnes/Tabor, The Practice of Statistics for the AP® Course, 7e, Unit 5, English

continuous random variable

Variable that can take any value in a specified interval on the number line. Continuous random variables are modeled by density curves.

density curve

Models the probability distribution of a continuous random variable with a curve that (a) is always on or above the horizontal axis and (b) has area exactly 1 underneath it. The area under the curve and above any specified interval of values on the horizontal axis gives the probability that the random variable falls within that interval.

normal random variable

A continuous random variable whose probability distribution is described by a normal curve.

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 values for an estimate (statistic).

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. The mean of the sampling distribution is also known as the expected value of the estimator.

sampling distribution of a sample proportion ρ̂

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

Large Counts condition

Let ρ̂ be the proportion of successes in a random sample of size n from a population with proportion of successes p. The Large Counts condition says that the sampling distribution of ρ̂ will be approximately normal when np ≥ 10 and n(1 - p) ≥ 10.

sampling distribution of a sample mean x

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

central limit theorem (CLT)

In an SRS of size n from any population with mean μ and finite standard deviation σ, when n is sufficiently large, the sampling distribution of the sample mean x is approximately normal.