Chap 5 Stat

45. For a population with a standard deviation of s = 12, a z-score of z= +0.50 corresponds to a score that is above the

T

53. On an exam with s =6, Tom's score of X = 54 corresponds to z=-1.00. The mean for the exam must be u = 60.

T

55. For a population of exam scores, a score of X=83 corresponds to z= +0.50 and a score of X= 89 corresponds to z= +1.50. The population mean is u = 80.

T

58. If an entire population of N= 20 scores is transformed into Z-scores, the set of 20 z-scores will have SX =0.

T

13. For a population with u = 100 and o=20, what is the X value corresponding to z=-0.75? a. 85 b. 95 c. 105 d. 115

A

2. On an exam with u = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution? a. o = 2 b. o=4 c. o=8 d. o= 10

A

21. For any distribution, what is the z-score corresponding to the mean? a. O b. 1 c. N d. Z

A

24. If an entire population with u = 60 and s = 8 is transformed into Z-scores, then the distribution of z-scores will have a mean of and a standard deviation of a. O and 1 b. 60 and 1 c. O and 8 d. 60 and 8 (unchanged)

A

26. Using z-scores, a population with u = 37 and s = 6 is standardized so that the new mean is u = 50 and s = 10. After the standardization, one individual has a score of X= 55. What was this individual's score in the original distribution? a. X = 40 b. X = 42 c. X = 43 d. It cannot be determined with the information given.

A

10. For a population with a standard deviation of o=6, what is the z-score corresponding to a score that is 12 points above the mean? a. z=1 b. z=2 c. z=6 d. z= 12

B

46. For a population with a mean of u = 80 and a standard deviation of o = 12, a score of X= 77 corresponds to z= 0.50.

F

49. In a distribution with u = 80 and s=20, a score of X= 95 corresponds to z=1.50. a. True b. False

F

64. For a sample with M = 50 and s = 8, z= 1.50 corresponds to X = 65.

F

70. In a sample with s =6, a score of X= 53 corresponds to z=-0.50. The mean for this sample is M= 50.

F

56. Because all z-score distributions have the same mean and standard deviation, the Z-score distribution is called a standardized distribution

T

What are the values for the population mean and standard deviation? a. m= 85 and s = 4 b. m = 85 and s = 2 c. m=81 and s = 4 d. m = 81 and s = 6

A

62. Standardized scores are "simple" values for the mean and standard deviation that do not change any individuals location within the distribution.

T

30. For a sample with M = 50 and s= 12, what is the X value corresponding to z=-0.25? a. 47 b. 53 c. 46 d. 54

A

33. In a sample with M = 40 and s=8, what is the z-score corresponding to X= 38? a. z=-0.25 b. z=-0.50 c. Z=0.25 d. z=0.50

A

35. For a sample with s = 12, a score of X= 73 corresponds to z= 1.00. What is the sample mean? a. M= 61 b. M=67 c. M= 79 d. M=85

A

4. Last week, Sarah had exams in Math, Spanish, and English. On the Math exam, the mean was u = 30 with s=5, and Sarah had a score of X= 45. On the Spanish exam, the mean was u = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was u = 70 with s = 8 and Sarah had a score of X= 70. For which class should Sara expect the better grade? a. Math b. Spanish c. English d. Grades are the same.

A

7. Which of the following represents the deviation score? a. X-u b. Z c. s d. (x- u)/s

A

8. Which of the following Z-score values represents the location closest to the mean? a. z= +0.50 b. z=+1.00 c. Z=-1.00 d. z=-2.00

A

75. On a psychology exam with u = 76 and 6 = 12, Tom scored 9 points below the mean, Mary had a score of X = 70, and Bill had a z-score of z=-1.00. Place these three students in order from lowest to highest score. _: Student with lowest score : Student with middle score : Student with highest score

ANSWER: Bill: X= 64, z=-1.00 Tom: X= 67, z=-0.75 Mary: X= 70, z=-0.50

76. For a distribution of scores, X = 40 corresponds to a z-score of z= +1.00, and X = 28 corresponds to a z-score of z= -0.50. What are the values for the mean and standard deviation for the distribution? (Hint: Sketch a distribution and locate each of the Z-score positions.)

ANSWER: The 12 points between the two scores corresponds to a total of 1.5 standard deviations. Therefore, s =8 and u = 32.

71. Describe the general purpose of a z-score and explain how a z-score accomplishes this goal.

ANSWER: The purpose of a z-score is to describe a location within a distribution using a single number. The z-score converts each X value into a signed number so that the sign tells whether the score is located above (+) or below (-) the mean, and the number identifies the distance from the mean by measuring the number of standard deviations between the score and the mean.

72. Describe what happens to the mean, the standard deviation, and the shape of a distribution when all of the scores are transformed into z-scores.

ANSWER: When an entire distribution of scores is transformed into z-scores, the resulting distribution will have a mean of zero, a standard deviation of one, and the same shape as the original distribution.

74. For a population with u = 48 and o=8, find the X value that corresponds to each of the following z-scores: -0.25, 1.50, 0.50, 2.00.

ANSWER: X= 46 (2 points below the mean) X= 36 (12 points below the mean) X = 52 (4 points above the mean) X=64 (16 points above the mean)

23. You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam? a. u = 60 and o= 10 b. u = 60 and o=5 c. u = 70 and o=10 d. u = 70 and o=5

B

25. A population with u = 85 and s = 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores? a. s = 12 b. s = 1.00 c. s=0 d. s = 4.

B

27. A distribution with u = 55 and s=6 is being standardized so that the new mean and standard deviation will be u = 50 and s = 10. When the distribution is standardized, what value will be obtained for a score of X = 58 from the original distribution? a. X= 53 b. X = 55 c. X=58 d. X=61

B

28. A distribution with u = 35 and s = 8 is being standardized so that the new mean and standard deviation will be u = 50 and s = 10. In the new, standardized distribution your score is X= 45. What was your score in the original distribution? a. X= 30 b. X=31 c. X= 39 d. X= 45

B

34. For a sample with M = 80, a score of X = 88 corresponds to z=2.00. What is the sample standard deviation? a. 2 b. 4 c. 8 d. 16

B

38. In N=25 games last season, the college basketball team averaged u = 76 points with a standard deviation of o=6. In their final game of the season, the team scored 89 points. Based on this information, the number of points scored in the final game was a. a little above average b. far above average c. above average, but it is impossible to describe how much above average d. impossible to determine because there is not enough information to compare last year with the average

B

6. What position in the distribution corresponds to a z-score of z= +2.00? a. Above the mean by 2 points b. Above the mean by a distance equal to 2 standard deviations c. Below the mean by 2 points d. Below the mean by a distance equal to 2 standard deviations

B

14. For a population with u = 80 and o= 10, what is the X value corresponding to z=-0.50? a. -5 b. 85 c. 75 d. 79.5

C

15. For a population with u = 40 and o=8, what is the X value corresponding to z=1.50? a. 44 b. 50 c. 52 d. 58

C

16. A population distribution has o=6. What position in this distribution is identified by a z-score of z=+2.00? a. two points above the mean b. two points below the mean c. twelve points above the mean d. twelve points below the mean

C

17. A population of scores has u = 44. In this population, a score of X = 40 corresponds to z=-0.50. What is the population standard deviation? a. 2 b. 4 c. 8 d. -8

C

32. A sample has M= 72 and s=4. In this sample, what is the X value corresponding to z=-2.00? a. X= 70 b. X=68 c. X = 64 d. X = 60

C

66. For a sample with a standard deviation of s = 6, a z-score of z=-1.50 corresponds to a location that is 9 points above the mean.

F

67. In a sample of n= 40 scores, X = 31 corresponds to z=-1.50 and X = 39 corresponds to z= +0.50. The sample mean is M = 36.

F

69. For a sample with a standard deviation of s=8, a score of X = 42 corresponds to z=-0.25. The mean for the sample is M = 40.

F

41. A score with a value less than or equal to the mean will have a z-score that is less than or equal to zero.

T

42. Any individual with a positive Z-score has a score greater than the mean. a. True b. False

T

43. If two individuals in the same population have identical X scores, they also will have identical z-scores.

T

44. For a population with a mean of u = 80, any score greater than 80 will have a positive z-score.

T

47. For any distribution of scores, the location identified by z=+1 and the location identified by z=-1 are exactly the

T

48. In a distribution with s=20, a score that is above the mean by 10 points will have a z-score of z=0.50.

T

51. In a population with s = 4, a score of X = 48 corresponds to z= 1.50. The mean for this population is u = 42.

T

52. On an exam, Tom scored 12 points above the mean and had a z-score of +2.00. The standard deviation for the set of exam scores must be s =6.

T

57. The process of transforming every x value in a distribution into a corresponding z-score to create a distribution of z scores is called a z-score transformation.

T

61. A professor standardizes exam scores so that all exams have u = 50 and s = 10. If the original scores from an exam have u = 42 and s = 6, then a student with an original exam score of X= 45 would receive a standardized score of X = 55.

T

63. For a sample with a mean of M = 50 and a standard deviation of s = 10, a z-score of z= +2.00 corresponds to X= 70.

T

65. For a sample with a standard deviation of s=10, a score with a deviation of +5 will have a z-score of z=0.50.

T

68. For a sample with a mean of M= 76, a score of X = 72 corresponds to z=-0.50. The sample standard deviation is s = 8.

T

77. A population of scores with u = 73 and s = 20 is standardized to create a new population with u = 50 and s = 10. What is the new value for each of the following scores from the original population? Scores: 63, 65, 77, 83 N X = 45

ANSWER: X= 63 X=65 N z=-0.50 z=-0.40 z= +0.20 z= +0.50 N X=83 N

73. For a population with u = 60 and o=12, find the z-score corresponding to each of the following X values: 66, 78, 57, 48.

ANSWER: z=+0.50 (above the mean by 1/2 standard deviation) z=+1.50 (above the mean by 1 1/2 standard deviations) z=-0.25 (below the mean by 1/4 standard deviation) z=-1.00 (below the mean by 1 standard deviation)

11. For a population with u = 80 and o=6, what is the z-score corresponding to X = 68? a. -0.50 b. -2.00 c. +2.00 d. -12.00

B

12. For a population with u = 40 and o=8, what is the z-score corresponding to X= 46? a. +0.50 b. +0.75 c. +1.00 d. +1.50

B

18. A population of scores has u = 80. In this population, a score of X = 86 corresponds to z=+2.00. What is the population standard deviation? a. 2 b. 3 c. 6 d. 12

B

19. In a population with o=8, a score of X = 44 corresponds to a Z-score of z=-0.50. What is the population mean? a. j = 36 b. u = 40 c. u = 48 d. u = 52

C

31. A sample of n=20 scores has a mean of M = 45 and a standard deviation of s = 8. In this sample, what is the z-score corresponding to X= 57? a. z= 12/20=0.60 b. z= 1.00 c. z= 1.50 d. z=2.00

C

1. On an exam with u = 52, you have a score of X = 44. Which of the following values for the standard deviation would give you the highest position in the class distribution? a. o = 2 b. o=4 c. O=8 d. o=10

D

22. A population has u = 50. What value of o would make X = 55 a more central, representative score in the population? a. o=1 b. o=5 c. o=10 d. o = 20

D

29. For an exam with a mean of M = 74 and a standard deviation of s= 8, Mary has a score of X= 80, Bob's score corresponds to z= +1.50, and Sue's score is located above the mean by 10 points. If the students are placed in order from smallest score to largest score, what is the correct order? a. Bob, Mary, Sue b. Sue, Bob, Mary c. Mary, Bob, Sue d. Mary, Sue, Bob

D

3. The direct, unchanged scores that are the direct result of measurement are called: a. standardized scores b. deviation scores c. Z-scores d. raw scores

D

36. For a sample of n= 30 scores, X = 45 corresponds to z= 1.50 and X= 40 corresponds to z= +1.00. What are the values for the sample mean and standard deviation? a. M= 35 and s = 10 b. M= 30 and s= 15 c. M= 35 and s= 15 d. M= 30 and s = 10

D

37. A sample with M = 85 and s = 12 is transformed into Z-scores. After the transformation, what are the values for the the mean and standard deviation for the sample of z-scores? a. M=85 and s = 12 b. M=0) and s = 12 c. M = 85 and s=1 d. M= 0 and s=1

D

39. Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean? a. When the population mean is much larger than 15 b. When the population standard deviation is much larger than 1 c. When the population mean is much smaller than 15 d. When the population standard deviation is much smaller than 15

D

40. Under what circumstances is a score that is located 5 points above the mean central value, relatively close to the mean? a. When the population mean is much less than 5 b. When the population mean is much greater than 5 c. When the population standard deviation is much less than 5 d. When the population standard deviation is much greater than 5

D

9. For a population with u = 80 and o=10, what is the Z-score corresponding to X = 95? a. +0.25 b. +0.50 c. +0.75 d. +1.50

D

50. For a population with u = 30, a score of X = 24 corresponds to z=-2.00. The standard deviation for the population is s=6

F

54. For a population with a mean of u = 40, a score of X = 37 corresponds to z=-0.50. The standard deviation for the population is s = 3.

F

59. A population with u = 45 and s = 8 is standardized to create a new distribution with u = 100 and s = 20. In this transformation, a score of X =41 from the original distribution will be transformed into a score of X = 110.

F

60. A population with u = 59 and s= 8 is standardized to create a new distribution with u = 100 and s = 20. After the transformation, an individual receives a new score of X = 90. The original score for this individual was X = 51.

F