Statistics Chapter 4
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 Sample A Sample B Both samples have the same standard deviation.
Both samples have the same standard deviation.
A researcher computes the definitional formula for SS, as finds that ∑(x-M)2 = 44. If this is a sample of 12 scores, then what would the value of sample variance be using the computational formula? 3.7 4.0 44
4.0
A researcher measures the time (in seconds) it takes a sample of 26 participants to respond to a stimulus presented on a computer screen. The standard deviation for response times is 6. In this example, what is the value for SS? 36 150 900 There is not enough information to answer this question.
900
The SIQR can be defined as the range of a distribution divided in half the IQR of a distribution plus the range a measure of half the distance between Q3 and Q1 all of the above
a measure of half the distance between Q3 and Q1
The range, a measure of variability, is the difference between the largest (L) and smallest (S) value in a list of scores is the most informative when used to describe data sets without outliers includes only two values in its computation, regardless of the number of scores in a distribution all of the above
all of the above
The sample variance is computed by dividing SS by ____; whereas the population variance is computed by dividing SS by ____. N; df df; n - 1 df; N n - 1; df
df; N
The variance and standard deviation can never be zero negative smaller than the mean larger than the mean
negative
An interquartile range removes the top and bottom 25% of scores in a distribution before calculating range scores above only the 75th percentile before calculating range scores below only the 25th percentile before calculating range all of the above
the top and bottom 25% of scores in a distribution before calculating range
A(n) ________ is a sample statistic that equals a population parameter on average. biased estimator degrees of freedom unbiased estimator sum of squares
unbiased estimator
Which of the following is an example of a distribution with NO variability? scores: 3, 5, 4, 4, 5, and 3 scores: 3, 3, 3, 3, 33, and 3 scores: 1, 2, 3, 4, 5, and 6 scores: 5, 5, 5, 5, 5, and 5
scores: 5, 5, 5, 5, 5, and 5
A researcher records the following motor assessment scores for two samples of athletes. Which sample has the largest standard deviation? Sample A: 8, 10, 12, 15, and 18 Sample B: 16, 18, 20, 23, and 26 Sample A Sample B Both samples have the same standard deviation.
Both samples have the same standard deviation.
hich of the following is consistent with the empirical rule? 68% of all scores lie within one standard deviation of the mean. 95% of all scores lie within two standard deviations of the mean. 99.7% of all scores lie within three standard deviations of the mean. all of the above
all of the above
Measures of variability can range in value from -∞ to + ∞ 0 to + ∞ It depends on whether the variability is positive or negative. It depends on the value of the mean for a given distribution.
0 to + ∞
A researcher records the following data: 4, 4, 4, 4, and 3. How would you describe the variability of the data? It is equal to zero because scores are approximately the same. It is negative because 3 is less than the other scores in the distribution. It is very small (close to 0) because scores are approximately the same. It is very large (much greater than 0) because 3 is an outlier in the data.
It is very small (close to 0) because scores are approximately the same.
all other things being equal, how will the value of the sample variance be different from the population variance? The sample variance will always be a smaller value than the population variance. The sample variance will always be a larger value than the population variance. The sample variance, but not the population variance, can be zero. The sample variance, but not the population variance, can be negative.
The sample variance will always be a larger value than the population variance.
Which of the following is the best explanation for why the standard deviation is almost always reported with the mean? The standard deviation measures the spread of scores from the mean, so it is important to know both the mean and the standard deviation. The standard deviation is also a measure of central tendency, so it is important to report this value with the mean. The mean and standard deviation estimate basically the same thing, so these values are typically reported together. This is not true; the standard deviation is rarely reported with the mean.
The standard deviation measures the spread of scores from the mean, so it is important to know both the mean and the standard deviation.
The degrees of freedom for the sample variance are equal to the sample size are equal to the sample size minus one can vary between - ∞ and + ∞ both B and C
are equal to the sample size minus one
A measure of the average squared distance of scores from the mean is called the range IQR variance sum of squares
variance
A researcher reports that the time (in minutes) it takes children who are "picky eaters" to finish their vegetables is negatively skewed, with children finishing their vegetables in 4.2±1.0 (M±SD) minutes. Based on Chebyshev's theorem, we can conclude that 68% of children finished their vegetables in 3.2 to 5.2 minutes. 50% of children finished their vegetables in at least 3.2 minutes. 99.7% of children finished their vegetables in 2.2 to 6.2 minutes. At least 89% of children finished their vegetables in 1.2 to 7.2 minutes.
At least 89% of children finished their vegetables in 1.2 to 7.2 minutes.
A researcher records the number of individual instruments identified by students listening to a piece of classical music. He splits the data into quartiles and reports that students correctly identified 3 instruments at the 25th percentile, 5 instruments at the 50th percentile, and 8 instruments at the 75th percentile. What are the IQR and SIQR for these data? the IQR is 3; the SIQR is 1.5 the IQR is 2; the SIQR is 1.0 the IQR is 5; the SIQR is 2.5 There is not enough information to answer this question.
the IQR is 5; the SIQR is 2.5
How is the sample variance computed differently from the population variance? only one formula includes a computation for SS the calculation in the numerator is different the calculation in the denominator is different both B and C
the calculation in the denominator is different
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? 17.5 3.5 232 not possible to know because the sample mean is not given
17.5
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? 1.0 (9.9 to 8.9) 0.3 (9.8 to 9.5) 0.5 (9.6 to 9.1) It is not possible to compute a range with an even number of scores.
1.0 (9.9 to 8.9)
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? 16 10 6 There is not enough information to answer this question.
16
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? 4 5 104
5
A researcher computes the definitional formula for SS, as finds that ∑(x-M)2 = 112. If this is a sample of 20 scores, then what would the value of population variance be using the computational formula? 5.6 5.9 112 not possible to know because the scores are not given
5.6
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 = 1,200. Assuming that a sample of 25 participants was observed in this study, what is the standard deviation for these data? 48 seconds 50 seconds 6.9 seconds 7.1 seconds
7.1 seconds
A psychologist treats 16 patients and records the number of sessions required to complete a behavioral therapy treatment for each patient. She computes SS = 800. Assuming the 16 patients constitute all patients under her care (so the population of her patients), what is the standard deviation for these data? 53.3 sessions 50 sessions 7.1 sessions 7.3 sessions
7.1 sessions
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? 68% of classes were between 68 and 80 decibels. 5% of classes were louder than 68 decibels. 95% of classes were between 68 and 92 decibels. all of the above
95% of classes were between 68 and 92 decibels.
Which of the following is a property of the standard deviation? The standard deviation varies between - ∞ and + ∞. The standard deviation is used to describe qualitative variables. Multiplying each score times the same constant will change the standard deviation by that constant. Adding the same constant to each score will change the standard deviation by that constant.
Multiplying each score times the same constant will change the standard deviation by that constant.
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? Sample A Sample B Both samples have the same variance. There is not enough information to answer this question.
Sample A
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 Sample A Sample B Both samples have the same standard deviation.
Sample A
A researcher records the following scores for attention during a video game task for two samples. Which sample has the largest standard deviation? Sample A: 10, 12, 14, 16, and 18 Sample B: 20, 24, 28, 32, and 36 Sample A Sample B Both samples have the same standard deviation.
Sample B
A reason for squaring deviations to compute SS in the numerator includes which of the following? The sum of the differences of scores from their mean is zero. The sum of the squared differences of scores from their mean is minimal. Squaring scores can be corrected easily by square rooting. all of the above
all of the above
The sample variance is: an unbiased estimator of the population variance associated with n - 1 degrees of freedom computed by dividing SS by df all of the above
all of the above
The sum of the squared deviations of scores from their mean is computed the same for samples and populations is computed by squaring each deviation to avoid a zero solution in the numerator is the numerator for the sample variance and population variance all of the above
all of the above
Which of the following describes the definitional formula for variance? It is stated in terms of how variance is defined. It is computed using SS in the numerator. It is a measure of the average squared distance that scores deviate from their mean. all of the above
all of the above
The definitional formula ______ the computational formula for SS. estimates explains diminishes equals
equals
A researcher measures the amount of coffee consumed by college students while studying during the final exam week. In her study, she found that students drink 2.3±0.8 (M±SD) cups of coffee per study session. Assuming the data are normally distributed, which of the following is the most appropriate conclusion? The average student drinks less than 2.3 cups of coffee per study session. Most students drink between 1.5 and 3.1 cups of coffee per study session. Most students drink between 2.3 and 3.9 cups of coffee per study session. Most students drink between 0.7 and 2.3 cups of coffee per study session.
Most students drink between 1.5 and 3.1 cups of coffee per study session.
Which of the following is true about the computational formula for variance? The computational formula will always produce the same solution as the definitional formula (give or take rounding errors). It is a short-cut method for calculating variance when the population or sample size is large. It is derived mathematically from the definitional formula. all of the above
all of the above
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? df = 24; it represents the number of scores that are free to vary in a sample. df = 23; it represents the number of scores that are free to vary in a sample. df = 23; dividing SS by df makes the sample variance a biased estimator of the population variance. df = 24; dividing SS by df makes the sample variance an unbiased estimator of the population variance.
df = 23; it represents the number of scores that are free to vary in a sample.
Why is it important to divide by df to compute sample variance? doing so makes the sample variance an unbiased estimator of the population variance doing so ensures that the value for sample variance varies between 0 and 1 doing so minimizes the likelihood that the sample variance will be a negative value it is not important; dividing by df is optional
doing so makes the sample variance an unbiased estimator of the population variance
The range of scores between the upper and lower quartiles of a distribution is called the median quartiles percentiles interquartile range
interquartile range
The advantage of squaring the deviation of each score from the mean and then summing is that it makes the sample variance an unbiased estimator of the population variance it makes the degrees of freedom for sample variance equal to n - 1 it produces a minimal positive solution that is not zero, so long as all scores are not exactly the same value both A and C
it produces a minimal positive solution that is not zero, so long as all scores are not exactly the same value
A researcher records a sample of 30 exam scores and finds that the population variance for these data is larger than the sample variance. Is this possible? yes, the population variance is usually larger than the sample variance no, the population variance will only be larger when at least 50 scores are recorded no, the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula not possible to know because the scores are not given
no, the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula
Which of the following values is NOT needed to compute sample variance using the computational formula, but is needed to compute the definitional formula? sample mean scores (x) sample size degrees of freedom
sample mean
Which of the following distributions has the largest variability? scores: 1, 3, 6, 9, and 12 scores: 22, 24, 26, 28, and 30 scores: 2, 3, 4, 5, and 6 scores: 1, 2, 3, 4, and 5
scores: 1, 3, 6, 9, and 12
All other things being equal (so assuming that the value of SS never changes), as sample size increases, the degrees of freedom for sample variance decrease the value of sample variance decreases the value in the numerator for sample variance increases the value in the denominator for sample variance decreases
the value of sample variance decreases
Regardless of the number of scores in a distribution, the range only includes ___ score(s) in its calculation. one two at most two the average
two
Each deviation in the numerator for variance is squared because without squaring each deviation, the solution for SS would be zero this inflates the value for variance, making it more accurate without squaring each deviation, the solution could be negative both A and C
without squaring each deviation, the solution for SS would be zero