# 9. Sampling Distribution of the Mean Flashcards Preview

## Stats > 9. Sampling Distribution of the Mean > Flashcards

Flashcards in 9. Sampling Distribution of the Mean Deck (23)
1
Q

Sampling Distribution of the Mean

A

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

2
Q

What does ̅X represent?

A

Sample Mean

Samples = normal alphabet

3
Q

What does µ represent?

A

Population mean

Populations = Greek Alphabet

4
Q

What does μ(petit ̅X) represent?

mu sub X-bar

A

Sampling distribution of the mean

5
Q

What does s represent?

A

Sample standard deviation

6
Q

What does σ represent?

A

Population standard deviation

7
Q

What does σ(petit ̅X) represent?

sigma sub X-bar

A

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

8
Q

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.
A
• µ
• mu sub X-bar
• ̅X
• sigma sub X-bar
• s
• σ
9
Q

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

A

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

10
Q

True or False?

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

A

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

11
Q

True or False?

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

A

True.

12
Q

True or False?

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

A

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

13
Q

True or False?

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

A

True.

14
Q

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

A

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

15
Q

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.

A

True.

16
Q

True or False?

The standard error of the mean (σ sub X-bar) measures varibility in a particular sample.

A

False. It measures variability among sample means.

17
Q

True or False?

The standard error of the mean (σ sub X-bar) increases in value with larger sample sizes.

A

False. It decreases in value with larger sample sizes.

18
Q

True or False?

The standard error of the mean (σ sub X-bar) equals 5, givent that σ = 40 and n = 64

A

True.

19
Q

Central Limit Theorem

A

Regardelss of the population shape, the shape of the sampling distribution of the mean approximates a normal curve if the sample size is sufficiently large.

20
Q

True or False?

The central limit theorem states that, with sufficiently large sample sizes, the shape of the population is normal.

A

False. The shape of the population remains the same regardless of sample size.

21
Q

True or False?

The central limit theorem states that, regardeless of sample size, the shape of the sampling distributions of the mean is normal.

A

False. It requires that the sample size be sufficiently large - usually between 25 and 100.

22
Q

True or False?

The central limit theorem ensures that the shape of the sampling distribution of the mean equals the shape of the population.

A

False. It ensures that the shape of the sampling distribution approximates a normal curve, regardless of the shape of the population (which remains intact).

23
Q

True or False?

The central limit theorem applies to the shape of the sampling distribution - not to the shape of the population and not to the shape of the sample.

A

True.