# 9. Sampling Distribution of the Mean Flashcards

Sampling Distribution of the Mean

Probability distribution of means for all possible random samples of a given size from some population.

What does ̅X represent?

Sample Mean

Samples = normal alphabet

What does µ represent?

Population mean

Populations = Greek Alphabet

What does μ(petit ̅X) represent?

mu sub X-bar

Sampling distribution of the mean

What does s represent?

Sample standard deviation

What does σ represent?

Population standard deviation

What does σ(petit ̅X) represent?

sigma sub X-bar

Standard of error of the mean, or simply the standard error.

Without peeking, list the special symbols for the:

- mean of the population
- mean of the sampling distribution of the mean
- mean of the sample
- standard error of the mean
- standard deviation of the sample
- standard deviation of the population.

- µ
- mu sub X-bar
- ̅X
- sigma sub X-bar
- s
- σ

Mean of the Sampling Distribution of the Mean (µ sub X-bar)

The mean of all samples means always equals the population mean.

True or False?

The mean of all sample means, µ sub X-bar, always equals the value of a particular sample mean.

False. It always equals the value of the population mean.

True or False?

The mean of all sample means, µ sub X-bar, equals 100 if, in fact, the population mean equals 100.

True.

True or False?

The mean of all sample means, µ sub X-bar, usually equals the value of a particular sample mean.

False. Because of chance, most sample means tend to be either larger or smaller than the mean of all sample means.

True or False?

The mean of all sample means, µ sub X-bar, is interchangeable with the population mean.

True.

Standard Error of the Mean (σ sub X-bar)

A rough measure of the average amount by which sample means deviate from the mean of the sampling distribution or from the population mean.

σ sub X-bar = σ / √n

True or False?

The standard error of the mean (σ sub X-bar) roughly measures the average amount by which sample means deviate from the population mean.

True.