PSYC*1010 Chapter 7: Probability and Samples

Question 1

What is a sampling error?

Answer 1

The natural discrepancy or expected amount of error between a sample statistic and its corresponding population parameter

Question 2

What is a distribution of sample means/sampling distribution?

Answer 2

The collection of sample means for all possible random samples of a particular size (n) that can be obtained from a population

Question 3

What are the three steps involved in constructing a distribution of sample means?

Answer 3

1. Select a random sample of a specific size from a population
2. Calculate the mean for that sample
3. Continue selecting samples and calculating means until all possible random samples have been included

Question 4

T or F: Sample means in a distribution should be less frequent around the population mean.

Answer 4

False. They should be most frequent around the population mean

Question 5

What type of distribution do sample means form?

Answer 5

A normal distribution

Question 6

As sample size increases, how do sample means change in relation to the population mean?

Answer 6

The larger the sample size, the closer the sample means should be to the population mean

Question 7

T or F: Means obtained from small samples should be more widely scattered in a distribution.

Answer 7

True

Question 8

What is the central limit theorem?

Answer 8

A mathematical theorem that specifies the characteristics of the distribution of sample means

Question 9

According to the central limit theorem, how will the mean of a distribution of sample means compare to the mean of the population?

Answer 9

The distribution of sample means will have the same mean as the population (μ)

Question 10

According to the central limit theorem, how will the standard deviation of sample means compare to the standard deviation of the population?

Answer 10

The standard deviation of sample means is equal to the population standard deviation divided by the square root of the sample size (σ/√n)

Question 11

What does the central limit theorem state about approaching a normal distribution of sample means?

Answer 11

Sample means will approach a normal distribution as n (sample size) approaches infinity

Question 12

The value of the central limit theorem comes from what two simple facts?

Answer 12

• The theorem describes the distribution of sample means for any population regardless of shape, mean, or standard deviation
• The distribution of sample means approaches a normal distribution very rapidly

Question 13

At what point/sample size is the distribution of sample means almost perfectly normal?

Answer 13

When n=30

Question 14

One of which two conditions must be met to assume normal distribution of sample means?

Answer 14

• The population from which the samples were selected is normally distributed
• The number of scores in each sample is 30 or more

Question 15

What is the expected value of M?

Answer 15

The mean of all sample means

Question 16

Why is the expected value of M an example of an unbiased statistic?

Answer 16

Because on average, the sample statistic produces a value exactly equal to the corresponding population parameter

Question 17

What is the notation for mean of sample means/expected value of M?

Answer 17

μ with subscript M

Question 18

Why is the mean of the distribution of sample means typically denoted as μ, even though it has its own notation?

Answer 18

Because the distribution of sample means is always equal to μ (population mean)

Question 19

What is the standard error of M?

Answer 19

The standard deviation of the distribution of sample means

Question 20

What is the notation for standard error of M?

Answer 20

σ with subscript M

Question 21

What does the standard error of M provide a measure of?

Answer 21

How much distance is expected, on average, between the sample mean and the population mean

Question 22

What does a small standard error indicate?

Answer 22

All sample means are close together and have similar values

Question 23

What does a large standard error indicate?

Answer 23

Sample means are scattered over a wide range and there are big differences from one sample to another

Question 24

Can standard error measure how well an individual sample mean represents the entire distribution?

Answer 24

Yes

Question 25

What two factors determine the magnitude of the standard error?

Answer 25

1. The size of the sample
2. The standard deviation of the population from which the sample was selected

Question 26

In relation to standard error, what does the law of large numbers state?

Answer 26

The larger the sample size (n), the more probable it is that the sample mean will be close to the population mean

Question 27

Does standard error increase or decrease in relation to the sample size?

Answer 27

Standard error decreases as sample size increases

Question 28

T or F: Standard error can be reduced by increasing sample size to around n=30, but increasing size above that doesn’t provide much additional improvement.

Answer 28

True

Question 29

What value for n produces the smallest possible sample from a population and largest standard error?

Answer 29

n=1

Question 30

As sample size increases, what happens to standard error?

Answer 30

It decreases

Question 31

What is the equation for standard error?

Answer 31

σM= σ/√n

Question 32

What is the primary use of the distribution of sample means?

Answer 32

To find the probability associated with any specific sample

Question 33

What does the z-score for sample means describe?

Answer 33

The distance of a sample mean from the population mean in terms of the number of standard deviations

Question 34

What is the equation for calculating the z-score of a sample mean?

Answer 34

z= (M- μ)/σM

Question 35

How does the z-score formula for a score in a population differ from the z-score formula for a sample mean?

Answer 35

Standard error must be used in the denominator when calculating z-scores for sample means, but standard deviation is used for a single score

Question 36

When the distribution of sample means is normal, what can be used to determine the probability of a sample mean occurring?

Answer 36

The z-score and unit normal table