Deck 7: Probability and Samples: The Distribution of Sample Means.

Question 1

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

Answer 1

80

Question 2

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

A)σM
B)µ
C)σ
D)MM

Answer 2

σM

Question 3

What is the expected value of M?

A)The sample mean
B)The sample standard deviation
C)The mean of the distribution of sample means
D)The standard deviation of the distribution of sample means

Answer 3

The mean of the distribution of sample means

Question 4

If random samples,each with n = 9 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 5

A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8,and the sample mean is M = 43.What is the expected value for the sample mean?

A)40
B)10
C)8
D)2

Question 6

A random sample of n = 60 scores is selected from a population.Which of the following distributions will definitely be normal?

A)The scores in the sample will definitely form a normal distribution.
B)The scores in the population definitely will form a normal distribution.
C)The distribution of sample means will definitely form a normal distribution.
D)None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.

Question 7

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

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

Question 8

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 9

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 10

Samples of n = 16 scores are selected from a population.If the distribution of sample means has an expected value of 40 and a standard error of 2,what is the mean and the standard deviation for the population?

A)µ = 40 and σ = 2
B)µ = 40 and σ = 8
C)µ = 40 and σ = 32
D)µ = 160 and σ = 2

Question 11

A random sample of n = 6 scores is selected from a population.Which of the following distributions will definitely be normal?

A)The scores in the sample will definitely form a normal distribution.
B)The scores in the population will definitely form a normal distribution.
C)The distribution of sample means will definitely form a normal distribution.
D)None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.

Question 12

For a particular population,a sample of n = 4 scores has a standard error of 6.For the same population,a sample of n = 16 scores would have a standard error of _____.

A)8
B)6
C)3
D)2

Question 13

What is the standard error of M?

A)The sample mean
B)The sample standard deviation
C)The mean of the distribution of sample means
D)The standard deviation of the distribution of sample means

Question 14

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 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)Only 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 = 4 scores is selected from a population with μ = 40 with σ = 8,and the sample mean is M = 43.What is the standard error for the sample mean?

A)8
B)4
C)3
D)2

Question 17

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 18

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
D)4 points

Question 19

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

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

Question 20

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,what is the average of all the sample means?

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

Question 21

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

A)M ≤38 for a sample of n = 4
B)M ≤36 for a sample of n = 4
C)M ≤38 for a sample of n = 100
D)M ≤36 for a sample of n = 100

Question 22

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

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

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)0.0062
B)0.9938
C)0.3085
D)0.6915

Question 25

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 26

If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12,what is the z-score corresponding to a sample mean of M = 73?

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

Question 27

A sample from a population with μ = 40 and σ = 8 has a mean of M = 36.If the sample mean corresponds to a z = -1.00,then how many scores are in the sample?

A)n = 64
B)n = 16
C)n = 8
D)n = 4

Question 28

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 29

A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18.If the sample mean is M = 76,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 30

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,what is the value of the sample mean?

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

Question 31

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

A)M ≤38 for a sample of n = 4
B)M≤ 36 for a sample of n = 4
C)M ≤38 for a sample of n = 100
D)M 36 for a sample of n = 100

Question 32

A sample is selected from a population with μ = 50 and σ = 12.If the sample mean of M = 56 produces a z-score of z = +1.00,then how many scores are in the sample?

A)2
B)4
C)9
D)16

Question 33

A sample of n = 36 scores is selected from a population with σ = 12.If the sample mean of M = 56 produces a z-score of z = +3.00,then what is the population mean?

A)50
B)52
C)54
D)56

Question 34

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 18.What is the probability that the sample mean will be greater than M = 43?

A)0.4325
B)0.3085
C)0.1587
D)0.0228

Question 35

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 36

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 37

A sample of n = 16 scores has a standard error of 4.What is the standard deviation of the population from which the sample was obtained?

A)64
B)16
C)4
D)2

Question 38

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 39

A random sample of n = 4 scores is obtained from a normal population with µ = 30 and σ = 8.What is the probability that the sample mean will be smaller than M = 22?

A)0.00003
B)0.0228
C)0.1587
D)0.3085

Question 40

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 41

A sample is selected from a normal population with μ = 50 and σ = 12.Which of the following samples would be considered extreme and unrepresentative for this population?

A)M = 53 and n = 16
B)M = 53 and n = 4
C)M = 56 and n = 16
D)M = 56 and n = 4

Question 42

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 43

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

Question 44

A sample is selected from a population with a mean of µ = 40.If the sample mean is M = 45,which of the following combinations would make the sample mean a good,representative value for the population?

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

Question 45

Samples of n = 9 scores are selected from a population.If the distribution of sample means has an expected value of 40,then the population has a mean of μ = 40.

Question 46

If the sample size is equal to the population variance (n = σ²),then the standard error is equal to 1.

Question 47

A sample is selected from a population with a mean of µ = 40.If the sample mean is M = 45,which of the following combinations would make the sample mean an extreme,unrepresentative value for the population?

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

Question 48

A sample of n = 4 scores is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 20.What is the probability of obtaining a sample mean greater than M = 48?

A)p = 0.6554
B)p = 0.3446
C)p = 0.5793
D)p = 0.4207

Question 49

Which combination of factors will produce the largest 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 50

Samples of n = 4 scores are selected from a population.If the distribution of sample means has a standard error σ = 5 points,then the population from which the samples were obtained has a standard deviation of σ = 20.

Question 51

A random sample of n = 9 scores is selected from a normal distribution with μ = 80 and σ = 12.What is the probability that the sample mean will be between 76 and 84?

A)0.9974
B)0.6826
C)0.3830
D)0.2586

Question 52

A random sample of n = 16 scores is selected from a normal distribution with μ = 500 and σ = 200.For this sample,which of the following is true?

A)p(402 < M < 598) = 0.95
B)p(425 < M < 575) = 0.95
C)p(450 < M < 550) = 0.95
D)p(490 < M < 510) = 0.95

Question 53

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

Question 54

In order for the distribution of sample means to be normal,it must be based on samples of at least n = 30 scores.

Question 55

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

Question 56

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 57

Samples of n = 16 are selected from a population.If the distribution of sample means has a standard error of 2 points,then the population has a standard deviation of σ = 8.

Question 58

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 59

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

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

Question 60

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

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

Question 61

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 62

A sample is selected from a population with µ = 30 and σ = 10.If the sample mean of M = 34 corresponds to z = +2.00,then the sample size is n = 25.

Question 63

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

Question 64

On average,a sample of n = 16 scores will provide a better estimate of the population mean than you would get with a sample of n = 9 scores from the same population.

Question 65

For a population with µ = 50 and ? = 6,describe the shape,the mean,and the standard deviation for the distribution of sample means for each of the following:

A)Samples of n = 4.
B)Samples of n = 36.

Question 66

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 67

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 68

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 69

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 70

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 71

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

Question 72

A sample of n = 9 scores is selected from a population with µ = 40 and σ = 18.If the sample mean corresponds to z = -1.00,then the sample mean is M = 31.

Question 73

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 74

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 75

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 greater than 72.

Question 76

If the sample size is increased,then the standard error for sample means will also increase.

Question 77

A sample of n = 4 scores is selected from a normal 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.

Question 78

If the sample size is doubled,the standard error will be cut in half.

Question 79

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 80

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