Deck 7: The Distribution of Sample Means

Question 1

What term is used to identify the standard deviation of the distribution of sample means?

A)the expected value of M
B)the standard error of M
C)the sample mean
D)the central limit mean

Answer 1

B

Question 2

What symbol is used to identify the standard error of M?

A)σ_M
B)µ
C)σ
D)M_M

Answer 2

A

Question 3

A random sample of n = 36 scores is selected from a population.Which of the following distributions definitely will be normal?

A)The scores in the sample will form a normal distribution.
B)The scores in the population will form a normal distribution
C)The distribution of sample means will form a normal distribution.
D)Neither the sample, the population, nor the distribution of sample means will definitely be normal.

Answer 3

C

Question 4

For a population with µ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ____.

A)5, 80
B)80, 5
C)20, 20
D)80, 1.25

Question 5

What happens to the expected value of M as sample size increases?

A)It also increases.
B)It decreases.
C)It stays constant.
D)The expected value does not change in a predictable manner when sample size increases.

Question 6

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the standard error for the distribution of sample means?

A)80
B)18
C)6
D)2

Question 7

A random sample of n = 4 scores is selected from a population.Which of the following distributions definitely will be normal?

A)The scores in the sample will form a normal distribution.
B)The scores in the population will form a normal distribution
C)The distribution of sample means will form a normal distribution.
D)Neither the sample, the population, nor the distribution of sample means will definitely be normal.

Question 8

The distribution of sample means ____ .

A)is always a normal distribution.
B)will be normal only if the population distribution is normal.
C)will be normal only if the sample size is at least n = 30.
D)we be normal if either the population is normal or the sample size is n > 30.

Question 9

If random samples, each with n = 36 scores, are selected from a normal population with µ = 80 and σ = 18, how much difference, on average, should there be between a sample mean and the population mean?

A)2 points
B)3 points
C)6 points
D)18 points

Question 10

What happens to the standard error of M as sample size increases?

A)It also increases.
B)It decreases.
C)It stays constant.
D)The standard error does not change in a predictable manner when sample size increases.

Question 11

For a particular population, a sample of n = 9 scores has a standard error of 8.For the same population, a sample of n = 16 scores would have a standard error of _____.

A)8
B)6
C)4
D)2

Question 12

If random samples, each with n = 4 scores, are selected from a normal population with µ = 80 and σ = 36, then what is the standard error for the distribution of sample means?

A)4
B)9
C)18
D)36

Question 13

Which combination of factors will produce the smallest value for the standard error?

A)a large sample and a large standard deviation
B)a small sample and a large standard deviation
C)a large sample and a small standard deviation
D)a small sample and a small standard deviation

Question 14

What term is used to identify the mean of the distribution of sample means?

A)the expected value of M
B)the standard error of M
C)the sample mean
D)the central limit mean

Question 15

Under what circumstances will the distribution of sample means be normal?

A)It is always normal.
B)only if the population distribution is normal
C)if the sample size is greater than 30
D)if the population is normal or if the sample size is greater than 30.

Question 16

A sample of n = 100 scores is selected from a population with μ = 80 with σ = 20.On average, how much error is expected between the sample mean and the population mean?

A)0.2 points
B)0.8 points
C)2 points
C)4 points

Question 17

If all the possible random samples with n = 36 scores are selected from a normal population with µ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means?

A)2
B)6
C)80
D)cannot be determined without additional information

Question 18

If random samples, each with n = 9 scores, are selected from a normal population with µ = 80 and σ = 36, then what is the expected value for the distribution of sample means?

A)4
B)12
C)16
D)80

Question 19

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the expected value for the distribution of sample means?

A)6
B)18
C)80/3
D)80

Question 20

A sample of n = 16 scores is selected from a population with μ = 80 with σ = 20.On average, how much error would be expected between the sample mean and the population mean?

A)20 points
B)5 points
C)4 points
D)1.25 points

Question 21

A sample obtained from a population with σ = 12 has a standard error of 2 points.How many scores are in the sample?

A)n = 36
B)n = 24
C)n = 6
D)n = 3

Question 22

If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12, then what is the z-score corresponding to a sample mean of M = 76?

A)z = 0.25
B)z = 0.50
C)z = 1.00
D)z = 2.00

Question 23

A random sample of n = 16 scores is obtained from a normal population with µ = 40 and σ = 8.What is the probability that the sample mean will be within 2 points of the population mean?

A)0.3830
B)0.6826
C)0.8664
D)0.9544

Question 24

A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18.If the sample mean is M = 76, then what is the z-score for the sample mean?

A)z = 0.33
B)z = 0.50
C)z = 1.00
D)z = 3.00

Question 25

For a normal population with µ = 40 and σ = 10 which of the following samples is least likely to be obtained?

A)M ≤ 42 for a sample of n = 4
B)M ≤ 44 for a sample of n = 4
C)M ≤ 42 for a sample of n = 100
D)M ≤ 44 for a sample of n = 100

Question 26

A random sample of n = 4 scores is obtained from a normal population with µ = 20 and σ = 4.What is the probability that the sample mean will be greater than M = 22?

A)0.50
B)1.00
C)0.1587
D)0.3085

Question 27

A sample of n = 4 scores is obtained from a population with μ = 70 and σ = 8.If the sample mean corresponds to a z-score of 2.00, then what is the value of the sample mean?

A)M = 86
B)M = 78
C)M = 74
D)M = 72

Question 28

A random sample of n = 4 scores is obtained from a population with a mean of µ = 80 and a standard deviation of σ = 10.If the sample mean is M = 90, what is the z-score for the sample mean?

A)z = 20.00
B)z = 5.00
C)z = 2.00
D)z = 1.00

Question 29

A sample from a population with μ = 40 and σ = 10 has a mean of M = 44.If the sample mean corresponds to a z = 2.00, then how many scores are in the sample?

A)n = 100
B)n = 25
C)n = 5
D)n = 4

Question 30

A random sample of n = 16 scores is obtained from a population with σ = 12.If the sample mean is 6 points greater than the population mean, what is the z-score for the sample mean?

A)+6.00
B)+2.00
C)+1.00
D)cannot be determined without knowing the population mean

Question 31

A sample is obtained from a population with μ = 100 and σ = 20.Which of the following samples would produce the most extreme z-score?

A)a sample of n = 25 scores with M = 102
B)a sample of n = 100 scores with M = 102
C)a sample of n = 25 scores with M = 104
D)a sample of n = 100 scores with M = 104

Question 32

A sample of n = 16 scores is obtained from a population with μ = 50 and σ = 16.If the sample mean is M = 54, then what is the z-score for the sample mean?

A)z = 0.25
B)z = 0.50
C)z = 1.00
D)z = 4.00

Question 33

A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32.If the sample mean is M = 104, what is the z-score for this sample mean?

A)2.00
B)1.00
C)0.50
D)0.25

Question 34

For a particular population a sample of n = 4 scores has an expected value of 10.For the same population, a sample of n = 25 scores would have an expected value of _____.

A)4
B)8
C)10
D)20

Question 35

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6.What is the probability that the sample mean will be greater than M = 43?

A)0.3085
B)0.6915
C)0.9332
D)0.0668

Question 36

A sample of n = 9 scores has a standard error of 6.What is the standard deviation of the population from which the sample was obtained?

A)54
B)18
C)6
D)2

Question 37

A sample of n = 4 scores has a standard error of 10 points.For the same population, what is the standard error for a sample of n = 16 scores?

A)1
B)2.5
C)5
D)10

Question 38

A sample of n = 4 scores is selected from a population with μ = 50 and σ = 12.If the sample mean is M = 56, what is the z-score for this sample mean?

A)0.50
B)1.00
C)2.00
D)4.00

Question 39

For a normal population with µ = 40 and σ = 10 which of the following samples has the highest probability of being obtained?

A)M ≤ 42 for a sample of n = 4
B)M ≤ 44 for a sample of n = 4
C)M ≤ 42 for a sample of n = 100
D)M ≤ 44 for a sample of n = 100

Question 40

For a normal population with a mean of µ = 80 and a standard deviation of σ = 10, what is the probability of obtaining a sample mean greater than M = 75 for a sample of n = 25 scores?

A)p = 0.0062
B)p = 0.9938
C)p = 0.3085
D)p = 0.6915

Question 41

As the sample size increase, the standard error also increases.

Question 42

In order for the distribution of sample means to be normal, it must be based on samples of at least n = 30 scores.
43 A sample of n = 25 scores is selected from a population with a mean of µ = 80 and a standard deviation of σ = 20.The expected value for the sample mean is 80.

Question 43

If the sample size is equal to the standard deviation (n = $\sigma$ ), then the standard error is equal to the square root of n.

Question 44

A sample of n = 25 scores is selected from a population with a mean of µ = 80 and a standard deviation of σ = 20.The standard error for the sample mean is 20.

Question 45

On average, a sample of n = 16 scores from a population with σ = 10 will provide a better estimate of the population mean than you would get with a sample of n = 16 scores from a population with σ = 5.

Question 46

The smallest possible standard error is obtained when a small sample is taken from a population with a small standard deviation.

Question 47

A sample of n = 9 scores is selected from a normal population with a mean of µ = 80 and a standard deviation of σ = 12.The probability that the sample mean will be greater than M = 86 is equal to the probability of obtaining a z-score greater than z = 1.50

Question 48

If samples are selected from a normal population, the distribution of sample means will also be normal.

Question 49

As the population standard deviation increases, the standard error will also increase.

Question 50

According to the central limit theorem, the standard error for a sample mean becomes smaller as the sample size increases.

Question 51

The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained.

Question 52

The mean for a sample of n = 9 scores has a standard error of 2 points.This sample was selected from a population with a standard deviation of σ = 18.

Question 53

A sample is obtained from a population with σ = 20.If the sample mean has a standard error of 5 points, then the sample size is n = 4.

Question 54

A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and σ = 18.This sample mean corresponds to a z?score of z = -1.00.

Question 55

If the standard deviation for a population increases, the standard error for sample means from the population will also increase.

Question 56

If the sample size is equal to the population standard deviation (n = $\sigma$ ), then the standard error for the sample mean is equal to 1.00.

Question 57

Two samples probably will have different means even if they are both the same size and they are both selected from the same population.

Question 58

The mean for a sample of n = 4 scores has a standard error σ = 5 points.This sample was selected from a population with a standard deviation of σ = 20.

Question 59

If samples of size n = 16 are selected from a population with μ = 40 and σ = 8, the distribution of sample means will have a standard error of 2 points.

Question 60

If samples of size n = 16 are selected from a population with μ = 40 and σ = 8, the distribution of sample means will have an expected value of 40.

Question 61

A population has µ = 60 and σ = 30.For a sample of n = 25 scores from this population, a sample mean of M = 55 would be considered an extreme value.

Question 62

A sample of n = 4 scores is selected from a population with μ = 70 and σ = 10.The probability of obtaining a sample mean greater than 65 is p = 0.8413.

Question 63

A sample of n = 16 scores is selected from a population with μ = 70 and σ = 8.It is very unlikely that the sample mean will be greater than 78.

Question 64

A sample of n = 4 scores is selected from a population with μ = 30 and σ = 8.The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00 from a normal distribution.

Question 65

A sample of n = 25 scores is selected from a population with μ = 50 and σ = 10.The probability of obtaining a sample mean greater than 55 is p = 0.3085.

Question 66

A sample of n = 25 scores is selected from a population with μ = 70 and σ = 20.It is very unlikely that the sample mean will be smaller than 72.

Question 67

A sample of n = 9 scores is selected from a population with μ = 50 and σ = 12.The probability of obtaining a sample mean greater than 46 is p = 0.8413.

Question 68

A sample of n = 9 scores is randomly selected from a population with µ = 80 and
σ = 9.If the sample mean is M = 83, then the corresponding z?score is z = +3.00.

Question 69

A population has µ = 60 and σ = 10.For a sample of n = 25 scores from this population, a sample mean of M = 55 would be considered an extreme value.