The sampling distribution of the mean and the standard error

Question 1

The bigger the sample size, the (more/less) spread out the sampling distribution of the mean is

Answer 1

Less (lower variability; closer to the mean of the population)

Question 2

How is the sampling distribution of the mean obtained?

Answer 2

Repeated sampling of the parent population

Question 3

What does the sampling distribution of the mean and the parent population have in common?

Answer 3

Mean

Question 4

What does the sampling distribution of the mean and the parent population have that is different?

Answer 4

Standard Distribution

Question 5

How do you calculate the standard distribution of the sampling distribution of the mean (SDM)?

Answer 5

Standard Deviation of Population / (square root of sample size)

Question 6

What does it mean when SDM is smaller than the population SD?

Answer 6

There is less sampling error (the standard error of the sample is smaller than the SD of the population)

Question 7

Complete the sentence:

For samples drawn at random of size N from a normal distribution with population mean mu and population s.d. sigma, the sampling distribution of the mean is (……..) with a mean (…….) and s.d. (…….)

Answer 7

1) Normal
2) mu
3) sd of population / square root of sample size

Question 7

Complete the sentence:

For samples drawn at random of size N from a normal distribution with population mean mu and population s.d. sigma, the sampling distribution of the mean is (……..) with a mean (…….) and s.d. (…….)

Answer 7

1) Normal
2) mu
3) sd of population / square root of sample size

Question 7

Complete the sentence:

For samples drawn at random of size N from a normal distribution with population mean mu and population s.d. sigma, the sampling distribution of the mean is (……..) with a mean (…….) and s.d. (…….)

Answer 7

1) Normal
2) mu
3) sd of population / square root of sample size

Question 7

Complete the sentence:

For samples drawn at random of size N from a normal distribution with population mean mu and population s.d. sigma, the sampling distribution of the mean is (……..) with a mean (…….) and s.d. (…….)

Answer 7

1) Normal
2) mu
3) sd of population / square root of sample size

Question 8

The IQ distribution of the population of visiting Ziltoidian aliens follows a normal distribution: N(130, 10). What is the standard deviation of the sampling distribution of the mean for samples from this population of size 16?

a.	30

b.	2.5

c.	7.5

d.	1.25

Answer 8

SDM = 10 / SQRT (16) = 2.5
SDM = 2.5

Answer = B

Question 9

Complete the sentence:

The sampling distribution of the mean describes a distribution of (……..) derived from samples of size N from a (………). The standard deviation of this distribution is commonly referred to as the (………) or (………) for short.

Answer 9

1) Sample means
2) Parent population
3) Standard Error of the Mean
4) Standard Error