Exam 1: Chapter 4

75. Measures of variability can range in value from

A) - to + B) 0 to + C) It depends on whether the variability is positive or negative. D) It depends on the value of the mean for a given distribution.

70. A researcher records the time in seconds it takes a sample of participants to walk alone through a dark portion of campus. The researcher computes SS = 1,000. Assuming that a sample of 11 participants was observed in this study, what is the standard deviation for these data?

A) 1 seconds B) 10 seconds C) 100 seconds D) 1000 seconds

77. A researcher records the following scores for an Olympic gymnast following her routine: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8. What is the range for the scores?

A) 1.0 (9.9 to 8.9) B) 0.3 (9.8 to 9.5) C) 0.5 (9.6 to 9.1) D) It is not possible to compute a range with an even number of scores.

69. A researcher decides to split scores on an exam into quartiles. She determines that a score of 64 is at the 25th percentile, a score of 74 is at the 50th percentile, and a score of 80 is at the 75th percentile. What is the interquartile range (IQR) for these data?

A) 16 B) 10 C) 6 D) There is not enough information to answer this question.

82. A researcher computes the computational formula for SS, as finds that x = 39 and x2 = 271. If this is a sample of 6 scores, then what would SS equal using the definitional formula?

A) 17.5 B) 3.5 C) 232 D) not possible to know because the sample mean is not given

81. A researcher computes the computational formula for SS, as finds that x = 22 and x2 = 126. If this is a sample of 4 scores, then what would SS equal using the definitional formula?

A) 4 B) 5 C) 104 D) not possible to know because the sample mean is not given

83. A researcher computes the definitional formula for SS, as finds that (x-M) = 112. If this is a sample of 20 scores, then what would the value of population variance be using the computational formula?

A) 5.6 B) 5.9 C) 112 D) not possible to know because the scores are not given

89. Which of the following is consistent with the empirical rule?

A) 68% of all scores lie within one standard deviation of the mean. B) 95% of all scores lie within two standard deviations of the mean. C) 99.7% of all scores lie within three standard deviations of the mean. D) all of the above

74. A researcher records the sound (in decibels) during a series of lessons taught by a substitute teacher at a local elementary school. In his study, he found that the sound was 80±6 (M±SD) decibels. Assuming the data are normally distributed, which of the following is an appropriate conclusion?

A) 68% of classes were between 68 and 80 decibels. B) 5% of classes were louder than 68 decibels. C) 95% of classes were between 68 and 92 decibels. D) all of the above

67. A researcher records the following data: 4, 4, 4, 4, and 3. How would you describe the variability of these data?

A) It is equal to zero because scores are approximately the same. B) It is negative because 3 is less than the other scores in the distribution. C) It is very small (close to 0) because scores are approximately the same. D) It is very large (much greater than 0) because 3 is an outlier in the data.

87. A researcher records the following scores on a working memory quiz for two samples. Which sample has the largest standard deviation? Sample A: 2, 3, 4, 5, 6, 7, and 8 Sample B: 4, 5, 6, 7, 8, 9, and 10

A) Sample A B) Sample B C) Both samples have the same standard deviation.

88. A researcher records the number of classroom interruptions during each of two class sessions. Which session has the largest standard deviation? Session A: 12, 15, 18, 24, and 30 Session B: 8, 10, 12, 16, and 20

A) Sample A B) Sample B C) Both samples have the same standard deviation.

71. A researcher measures the number of trials it takes two samples of participants to master a new task. In both samples, SS = 240. Sample A consisted of 12 participants and Sample B consisted of 18 participants. Which sample is associated with the largest variance?

A) Sample A B) Sample B C) Both samples have the same variance. D) There is not enough information to answer this question.

72. Which of the following is true about the computational formula for variance?

A) The computational formula will always produce the same solution as the definitional formula (give or take rounding errors). B) It is a short-cut method for calculating variance when the population or sample size is large. C) It is derived mathematically from the definitional formula. D) all of the above

86. The sample variance is:

A) an unbiased estimator of the population variance B) associated with n - 1 degrees of freedom C) computed by dividing SS by df D) all of the above

92. The degrees of freedom for the sample variance

A) are equal to the sample size B) are equal to the sample size minus one C) can vary between - and + D) both B and C

73. A researcher selects a sample of 24 participants and has them complete a survey on dating preferences. In this example, what are the degrees of freedom for sample variance and what does this figure represent?

A) df = 24; it represents the number of scores that are free to vary in a sample. B) df = 23; it represents the number of scores that are free to vary in a sample. C) df = 23; dividing SS by df makes the sample variance a biased estimator of the population variance. D) df = 24; dividing SS by df makes the sample variance an unbiased estimator of the population variance.

84. The definitional formula ______ the computational formula for SS.

A) estimates B) explains C) diminishes D) equals

68. Regardless of the number of scores in a distribution, the range only includes ___ score(s) in its calculation.

A) one B) two C) at most two D) the average

76. Which of the following distributions has the largest variability?

A) scores: 1, 3, 6, 9, and 12 B) scores: 22, 24, 26, 28, and 30 C) scores: 2, 3, 4, 5, and 6 D) scores: 1, 2, 3, 4, and 5

91. Which of the following is an example of a distribution with NO variability?

A) scores: 3, 5, 4, 4, 5, and 3 B) scores: 3, 3, 3, 3, 33, and 3 C) scores: 1, 2, 3, 4, 5, and 6 D) scores: 5, 5, 5, 5, 5, and 5

80. All other things being equal (so assuming that the value of SS never changes), as sample size increases,

A) the degrees of freedom for sample variance decrease B) the value of sample variance decreases C) the value in the numerator for sample variance increases D) the value in the denominator for sample variance decreases

78. An interquartile range removes

A) the top and bottom 25% of scores in a distribution before calculating range B) scores above only the 75th percentile before calculating range C) scores below only the 25th percentile before calculating range D) all of the above

85. Each deviation in the numerator for variance is squared because

A) without squaring each deviation, the solution for SS would be zero B) this inflates the value for variance, making it more accurate C) without squaring each deviation, the solution could be negative D) both A and C

79. The variance and standard deviation can never be

A) zero B) negative C) smaller than the mean D) larger than the mean