Essential Statistics for the Behavioral Sciences
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1.A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called
A) a conditional procedure
B) a sampling distribution
C) sampling without replacement
D) random sampling
2. What values are distributed along the x-axis for a sampling distribution of the sample mean?
A) scores
B) sample means
C) sample variances
D) both B and C
3. What values are distributed along the x-axis for a sampling distribution of the sample variance?
A) scores
B) sample means
C) sample variances
D) both B and C
4. A sampling distribution of the sample mean or variance is
A) a distribution of all measures that could be obtained in a given sample of a given size
B) a distribution of all scores that could be obtained in samples of a given size from one or more populations
C) a distribution of all scores that could be obtained in a population
D) a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population
5. A researcher selects from a participant pool of 4 males and 6 females. He determines that the probability of selecting 2 male participants is p = .16. Based on this probability, what strategy did the researcher use to sample participants.
A) sampling with replacement
B) sampling without replacement
6. A researcher selects from a participant pool of 4 males and 6 females. He determines that the probability of selecting 2 female participants is p = .30. Based on this probability, what strategy did the researcher use to sample participants.
A) sampling with replacement
B) sampling without replacement
7. In terms of characterizing samples, statistical theory was developed using a sampling strategy in which
A) the order of selecting participants matters
B) the same participant can be selected twice in the same sample
C) participants are replaced after being sampled
D) all of the above
8 Experimental research is typically conducted using a sampling strategy in which
A) the order of selecting participants matters
B) the same participant can never be selected twice in the same sample
C) participants are replaced after being sampled
D) all of the above
9. Suppose you select a sample of three people from a population of four (A, B, C, D). Which of the following samples is possible using the experimental sampling strategy?
A) persons A, C, and A
B) persons A, D, and D
C) persons B, C, and D
D) persons B, A, and B
10. A researcher selects a sample of size 6 from a population of size 10. How many possible samples of this size can be selected using theoretical sampling?
A) 100,000
B) 1,000,000
C) 10,000,000
D) over 60,000,000 samples
11. A researcher selects a sample of size 4 from a population of size 6. How many possible samples of this size can be selected using experimental sampling?
A) 15
B) 30
C) 1,296
D) 4,096
12. Which type of sampling is most often applied by researchers in the behavioral sciences?
A) theoretical sampling
B) normal sampling
C) experimental sampling
D) standard normal sampling
13 What does it mean to say that the sample mean is an unbiased estimator of the population mean?
A) The sample means will vary minimally from the population mean.
B) The sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population.
C) If we select a sample at random, then on average we can expect the sample mean to equal the population mean.
D) all of the above
14. What is the central limit theorem?
A) It explains that sample means will vary minimally from the population mean.
B) It explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population.
C) It explains that if we select a sample at random, then on average we can expect the sample mean to equal the population mean.
D) all of the above
15. It happens to be the case that the standard error of the sampling distribution of sample means
A) is minimal
B) is approximately equal to that in the population
C) gets larger as the sample size increases
D) both A and C
16 Regardless of the distribution of the population, the sampling distribution of sample means will be approximately normally distributed. What characteristic of the mean explains this?
A) unbiased estimator
B) central limit theorem
C) minimal variance
D) none of the above
17 A researcher randomly selects a sample of athletes and reports that their average score on a health and fitness scale is 23. Based on the characteristics of the sample mean, what does this say about the mean in the population?
A) Nothing; it was just a sample.
B) There is no way to know without knowing the size of the sample.
C) It tells us that the mean in the population is no less than 23.
D) We expect that the population mean is equal to 23 because the sample mean is an unbiased estimator of the population mean.
18. The shape of the sampling distribution of the mean is approximately ________, whereas the shape of the sampling distribution of the variance is approximately ________.
A) normal; normal
B) positively skewed; normal
C) normal; positively skewed
D) positively skewed; positively skewed
19. The sampling distribution of the mean and the sampling distribution of the variance (when dividing SS by n - 1)
A) are both unbiased estimators
B) both follow the central limit theorem
C) are both associated with minimal variance
D) all of the above
20. A researcher randomly selects a sample of participants from a population with a variance of 4. If a researcher selects a sample of 16 participants with a mean of 12, then what is the mean and standard error for the sampling distribution of the mean?
A) mean = 12, standard error = 2
B) mean = 12, standard error = 1
C) mean = 12, standard error = 0.5
D) There is not enough information to answer this question.
21. The mean of the sampling distribution of sample means is
A) equal to the population mean
B) equal to the population variance
C) both A and B
D) none of the above
22. A researcher selects a sample of 64 participants from a population with a mean of 10 and a variance of 16. What is the standard error of the mean?
C) 0.5
D) There is not enough information to answer this question.
23 A researcher selects a sample of 121 participants from a population with a mean of 32 and a standard deviation of 22. What is the standard error of the mean? A) 32
B) 2.0
C) 0.5
D) There is not enough information to answer this question.
24. A researcher selects two samples of 64 participants each. In the first sample the population mean was 10 and the variance was 16. In this second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean?
A) Sample 1
B) Sample 2
C) None, both samples will have the same value for standard error
D) There is not enough information to answer this question.
25. A researcher selects two samples of 25 participants each. In the first sample the population mean was 32 and the variance was 8. In this second sample, the population mean was 4 and the variance was 8. Which sample will be associated with a larger standard error of the mean?
A) Sample 1
B) Sample 2
C) None, both samples will have the same value for standard error
D) There is not enough information to answer this question.
26. Two researchers select a sample for a population with a mean of 12.4 and a standard deviation of 9. Researcher A selects a sample of 30 participants. Researcher B selects a sample of 40 participants. Which sample is associated with a smaller standard error?
A) Researcher A's, because the sample size was smaller.
B) Researcher B's, because the sample size was smaller.
C) Researcher A's, because the sample size was larger.
D) Researcher B's, because the sample size was larger.
27. As sample size increases, the standard error of the mean
A) increases
B) decreases
C) can increase or decrease
D) does not change
28. The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?
Researcher A: n = 36, = 12, = 9
Researcher B: n = 36, = 12, = 6
A) Researcher A
B) Researcher B
C) They both have the same standard error.
29 The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?
Researcher A: n = 18, = 8, = 2.4
Researcher B: n = 12, = 8, = 2.4
A) Researcher A
B) Researcher B
C) They both have the same standard error.
30. The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?
Researcher A: n = 25, = 5, = 7
Researcher B: n = 25, = 32, = 7
A) Researcher A
B) Researcher B
C) They both have the same standard error.
31 Each of the following statements are true, except that
A) increasing the sample size will decrease standard error
B) the larger the sample size, the larger the standard error
C) the larger the standard deviation in the population, the larger the standard error
D) both B and C
32 Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means?
A) the central limit theorem
B) the skewed distribution rule
C) the fact that sample means vary minimally from the population mean
D) the fact that increasing sample size will decrease standard error
33. A researcher increases the sample size, which will:
A) increase the value of standard error
B) decrease the value of standard error
C) reduce variability in the population
D) increase variability in the population
34. Because the sampling distribution of sample means is normally distributed, we can use the z transformation formula to find probabilities. Which of the following gives the appropriate notation for this formula? A)
B)
C)
D) all of the above
35. A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean of 13 or larger from this population?
A) equal to the probability of selecting a score above the mean
B) about one standard deviation below the mean
C) less than .03
D) greater than .31
36. A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean that is at least equal to the population mean?
A) .50
B) equal to the probability of selecting a sample mean that is at most equal to the population mean
C) both A and B
D) none of the above
37. A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean that is at least two standard deviations larger than the population mean?
A) .0228
B) .4772
C) .9772
D) equal to the probability of selecting a sample mean that is at least two standard deviations below the mean
38. A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean equal to at least 12?
A) less than 1%
B) greater than 50%
C) about the same as selecting a sample mean that is at least equal to the population mean
D) equal to the probability of selecting a sample mean that is smaller than 8
39. A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between a sample mean of
A) 34 and 40
B) 34 and 38
C) 38 and 44
D) 36 and 40
40. A researcher selects a sample of 9 participants from a population with a mean of 8 and a standard deviation of 3. About 14% of the sample means in this sampling distribution should be between a sample mean of
A) 6 and 8
B) 5 and 6
C) 9 and 10
D) 10 and 11
41. How is the standard error of the mean typically reported in a graph?
A) using error bars
B) by plotting sample means
C) by listing group names along the x-axis
D) it is never reported in a graph
42. An articles states that a sample of 40 participants took 12 ± 2.3 (M ± SEM) seconds to complete a cognitive assessment. Which value is the standard error of the mean?
A) 40
B) 12
C) 2.3
D) The standard error of the mean is not reported in the article
43. A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM) dollars on groceries each week. Which value is the standard error of the mean?
A) 112
B) 40
C) 100
D) The standard error of the mean is not reported in the article
T F 44. A sample mean is not always equal to a population mean.
T F 45 A sampling distribution is a distribution of scores in a population.
T F 46. A sampling distribution is a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population.
T F 47 Researchers typically sample with replacement, although the development of statistical theory was based on the use of sampling without replacement.
T F 48. For the experimental sampling strategy, the order in which a participant is selected does not matter, and once selected, each participant is not replaced before sampling again.
T F 49 There are more possible samples that can be selected using theoretical sampling than using experimental sampling for any sample size greater than 1.
T F 50. There are 25 possible samples of size 2 that can be selected from a population of 5 people using theoretical sampling.
T F 51. The central limit theorem states that the sample mean will equal the population mean on average.
T F 52 The sampling distribution of the mean has minimum variance.
T F 53. The sampling distribution of the mean is a distribution of all the possible samples of a particular size that can be selected from a given population.
T F 54. The sample mean is an unbiased estimator, follows the central limit theorem, and has minimum variance
T F 55 The sample mean is an unbiased estimator of the population mean.
T F 56. If a researcher selects a sample with a mean of 8, then the mean of the sampling distribution of possible sample means will also equal 8.
T F 57 If a researcher selects a sample of 64 participants from a population with a variance of 16, then the standard error of the mean will be 2.0.
T F 58. The mean of a sampling distribution of sample means equals the population mean from which the samples were selected.
T F 59. The standard error is the sample standard deviation divided by the square root of the sample size.
T F 60. The standard error of the mean is the standard deviation in a sampling distribution of sample means.
T F 61 A researcher wants to select a sample of 30 participants from one of two populations. In Population A, the standard deviation is 12. In Population B, the standard deviation is 4. In this example, selecting a sample from Population A will produce the smallest standard error.
T F 62. As sample size increases, standard error decreases.
T F 63. As sample size decreases, the standard error also decreases.
T F 64 The larger the population standard deviation, the smaller the standard error of the mean will be.
T F 65. A researcher selects a sample of 625 participants from a population with a mean of 120 and a standard deviation of 25. The probability of selecting a sample mean that is larger than 125 is close to zero.
T F 66. A researcher selects a sample of 169 participants from a population with a mean of 50 and a standard deviation of 13. The probability of selecting a sample mean that is less than 49 is .8413.
T F 67. A z transformation can be computed to locate sample means in a sampling distribution
T F 68. The standard error of the mean is typically reported in a table or graph, but never in the text of a research article.
T F 69 If data are reported as 12 ± 20 (M ± SEM), then the standard error of the mean is equal to 20.
Answer Key
1. B
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2. B
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3. C
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4. D
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5. A
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6. B
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7. D
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8 B
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9 C
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10. B
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11. A
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12. C
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13. C
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14. B
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15 A
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16 B
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17. D
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18. C
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19. A
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20. C
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21. A
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22 C
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23. B
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24. A
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25 C
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26 D
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27. B
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28. B
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29. A
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30. C
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31. B
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32 A
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33 B
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34. D
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35. C
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36. C
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37. A
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38. D
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39 D
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40 C
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41. A
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42. C
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43. B
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44. True
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45 False
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46. True
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47. False
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48 True
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49 True
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50. False
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51. False
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52. True
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53. True
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54. True
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55 True
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56 True
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57. False
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58. True
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59. False
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60. True
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61. False
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62 True
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63 False
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64. False
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65. True
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66. False
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67. True
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68 False
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