AP Statistics – Chapter 7: Sampling Distributions

This set of flashcards covers key terms and definitions related to Sampling Distributions in AP Statistics.

Parameter

A number that describes some characteristic of the population.

Statistic

A number that describes some characteristic of a sample.

Unbiased Estimator

A statistic is called an unbiased estimator of a parameter if the mean of its sampling distribution is equal to the parameter being estimated.

Sampling Distribution

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

Mean of Sampling Distribution

The mean of a sampling distribution will always equal the mean of the population for any sample size.

Spread of Sampling Distribution

The spread is affected by the sample size; larger sample sizes result in smaller spread or variability.

Sample Proportion (𝑝̂)

The proportion of the sample having a characteristic of interest.

Conditions for using 𝜎!

Use this formula only when the size of the sample is no more than 10% of the population size.

Large Counts Condition

We will use normal approximation if n and p satisfy n*p ≥ 10 and n(1 − p) ≥ 10.

Mean of Sample Means (𝑥̅)

The mean of the sampling distribution of 𝑥̅ is equal to the population mean 𝜇.

Standard Deviation of Sample Means (𝜎)̅

The standard deviation of the sampling distribution of 𝑥̅ is equal to 𝜎/√n.

Central Limit Theorem

If an SRS is drawn from any population with n large (n ≥ 30), the sampling distribution of 𝑥̅ is approximately Normal.

10% Condition

Use formula for standard deviation of the sample proportion when the sample size is no more than 10% of the population size.