Deck 7: Probability and Samples: the Distribution of Sample Means
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Deck 7: Probability and Samples: the Distribution of Sample Means
1
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.
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.
It decreases.
2
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)will be normal if either the population is normal or the sample size is n > 30
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)will be normal if either the population is normal or the sample size is n > 30
will be normal if either the population is normal or the sample size is n > 30
3
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.
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.
It stays constant.
4
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
A)the expected value of M
B)the standard error of M
C)the sample mean
D)the central limit mean
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5
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
A)the expected value of M
B)the standard error of M
C)the sample mean
D)the central limit mean
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6
Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the expected value of M,the mean of the distribution of sample means?
A)6
B)18
C)80/3
D)80
A)6
B)18
C)80/3
D)80
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7
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
A)20 points
B)5 points
C)4 points
D)1.25 points
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8
A random sample of n = 36 scores is selected from a population.Which of the following distributions will definitively 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)None of the distributions - the sample, the population, the distribution of sample means - will definitely 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)None of the distributions - the sample, the population, the distribution of sample means - will definitely be normal.
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9
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
A)0.2 points
B)0.8 points
C)2 points
D)4 points
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10
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)It cannot be determined without additional information.
A)2
B)6
C)80
D)It cannot be determined without additional information.
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11
A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively 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)None of the distributions - the sample, the population, the distribution of sample means -will definitely 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)None of the distributions - the sample, the population, the distribution of sample means -will definitely be normal.
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12
Under what circumstances is distribution of sample means 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
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
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13
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 of the mean of the distribution of sample means?
A)4
B)12
C)16
D)80
A)4
B)12
C)16
D)80
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14
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
A)2 points
B)3 points
C)6 points
D)18 points
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15
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
A)8
B)6
C)4
D)2
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16
What symbol is used to identify the standard error of M?
A)σM
B)µ
C)σ
D)MM
A)σM
B)µ
C)σ
D)MM
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17
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
A)80
B)18
C)6
D)2
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18
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
A)5; 80
B)80; 5
C)20; 20
D)80; 1.25
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19
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
A)4
B)9
C)18
D)36
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20
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
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
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21
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)It cannot be determined without knowing the population mean.
A)+6.00
B)+2.00
C)+1.00
D)It cannot be determined without knowing the population mean.
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22
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
A)p = 0.0062
B)p = 0.9938
C)p = 0.3085
D)p = 0.6915
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23
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
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
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24
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
A)M = 86
B)M = 78
C)M = 74
D)M = 72
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25
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
A)z = 0.33
B)z = 0.50
C)z = 1.00
D)z = 3.00
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26
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
A)z = 0.25
B)z = 0.50
C)z = 1.00
D)z = 4.00
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27
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
A)n = 36
B)n = 24
C)n = 6
D)n = 3
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28
For a particular population a sample of n = 4 scores has an expected mean value of 10.For the same population,a sample of n = 25 scores would have an expected mean value of ____.
A)4
B)8
C)10
D)20
A)4
B)8
C)10
D)20
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29
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
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
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30
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
A)1
B)2.5
C)5
D)10
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31
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
A)0.3830
B)0.6826
C)0.8664
D)0.9544
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32
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
A)54
B)18
C)6
D)2
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33
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
A)z = 0.25
B)z = 0.50
C)z = 1.00
D)z = 2.00
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34
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
A)n = 100
B)n = 25
C)n = 5
D)n = 4
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35
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
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
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36
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
A)z = 20.00
B)z = 5.00
C)z = 2.00
D)z = 1.00
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37
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
A)2.00
B)1.00
C)0.50
D)0.25
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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
A)0.50
B)1.00
C)2.00
D)4.00
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39
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
A)0.50
B)1.00
C)0.1587
D)0.3085
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40
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
A)0.3085
B)0.6915
C)0.9332
D)0.0668
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41
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.
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42
If samples are selected from a normal population,the distribution of sample means will also be normal.
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43
A mathematical proposition known as the central limit theorem provides a precise description of the distribution that would be obtained if you selected every possible sample,calculated every sample mean,and constructed the distribution of the sample mean.
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44
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.
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45
The mean for a sample of n = 4 scores has a standard error σM = 5 points.This sample was selected from a population with a standard deviation of σ = 20.
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46
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.
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47
The smallest possible standard error is obtained when a small sample is taken from a population with a small standard deviation.
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48
On average,a sample of n = 16 scores from a population with s = 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 s = 5.
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49
The law of large numbers states that the larger the sample size (n),the more probable it is that the sample mean will be close to the population mean..
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50
A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and s = 18.This sample mean corresponds to a z-score of z = -1.00.
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51
The distribution of sample means is the collection of sample means for all the possible random samples of a particular size (n)that can be obtained from a population.
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52
If the sample size is equal to the population standard deviation (n = s),then the standard error for the sample mean is equal to 1.00.
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53
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 s = 18.
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54
A sample is obtained from a population with s = 20.If the sample mean has a standard error of 5 points,then the sample size is n = 4.
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55
As the sample size increases,the standard error also increases.
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56
If the standard deviation for a population increases,the standard error for sample means from the population will also increase.
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57
According to the central limit theorem,the standard error for a sample mean becomes smaller as the sample size increases.
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58
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.
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59
The sampling error is the natural discrepancy,or amount of error,between a sample statistic and its corresponding population parameter.
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60
Two samples probably will have different means even if they are both the same size and they are both selected from the same population.
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61
A sample of n = 16 scores is selected from a normal population with µ = 40 and σ = 12.
a. Describe the distribution of sample means that contains the mean for the sample.
b. What is the probability that the sample mean will be greater than 43?
c. What is the probability that the sample mean will be less than 34?
a. Describe the distribution of sample means that contains the mean for the sample.
b. What is the probability that the sample mean will be greater than 43?
c. What is the probability that the sample mean will be less than 34?
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62
A sample of n = 9 scores is randomly selected from a population with µ = 80 and s = 9.If the sample mean is M = 83,then the corresponding z-score is z = +3.00.
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63
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.
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64
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.
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65
Describe what is measured by the standard error of M.
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66
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.
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67
Define the distribution of sample means.
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68
Describe the shape,the mean,and the standard deviation for each of the following two distributions.
a. A population of scores with µ = 50 and σ = 6.
b. The distribution of sample means based on samples of n = 36 selected from a population with µ = 50 and σ = 6.
a. A population of scores with µ = 50 and σ = 6.
b. The distribution of sample means based on samples of n = 36 selected from a population with µ = 50 and σ = 6.
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69
A sample of n = 4 scores is selected from a population with µ = 70 and s = 10.The probability of obtaining a sample mean greater than 65 is p = 0.8413.
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70
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.
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71
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.
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72
A sample of n = 4 scores is selected from a population with µ = 30 and s = 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.
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73
A sample of n = 9 scores is selected from a normal population with a mean of µ = 80 and a standard deviation of s = 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.
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74
Each of the following samples was obtained from a population with µ = 100 and σ = 10.Find the z-score corresponding to each sample mean.
a. M = 95 for a sample of n = 4
b. M = 104 for a sample of n = 25
c. M = 103 for a sample of n = 100
a. M = 95 for a sample of n = 4
b. M = 104 for a sample of n = 25
c. M = 103 for a sample of n = 100
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75
For a normal population with µ = 100 and σ = 20:
a. What is the probability of obtaining a sample mean greater than 110 for a sample of n = 4 scores?
b. What is the probability of obtaining a sample mean greater than 110 for a sample of n = 16 scores?
c. For a sample of n = 25 scores, what is the probability that the sample mean will be within 5 points of the population mean? In other words, what is p(95 < M < 105)?
a. What is the probability of obtaining a sample mean greater than 110 for a sample of n = 4 scores?
b. What is the probability of obtaining a sample mean greater than 110 for a sample of n = 16 scores?
c. For a sample of n = 25 scores, what is the probability that the sample mean will be within 5 points of the population mean? In other words, what is p(95 < M < 105)?
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76
A population has a mean of µ = 80 with σ = 20.
a. If a single score is randomly selected from this population, how much distance, on average, should you find between the score and the population mean?
b. If a sample of n = 4 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean?
c. If a sample of n = 100 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean?
a. If a single score is randomly selected from this population, how much distance, on average, should you find between the score and the population mean?
b. If a sample of n = 4 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean?
c. If a sample of n = 100 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean?
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77
A sample of n = 9 scores is selected from a population with µ = 50 and s = 12.The probability of obtaining a sample mean greater than 46 is p = 0.8413.Z
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