stats chapter 4
The degrees of freedom for the sample variance ______.
. are equal to the sample size minus one
Measures of variability can range in value from ______.
0 to + infinity
A researcher computes the computational formula for SS, as finds that = 39 and = 271. If this is a sample of six scores, then what would SS equal using the computational formula?
17.5
A researcher computes the definitional formula for SS, as finds that = 44. If this is a sample of 12 scores, then what would the value of sample variance be using the definitional formula?
4.0
A researcher computes the computational formula for SS, as finds that = 22 and = 126. If this is a sample of four scores, then what would SS equal using the computational formula?
5
A researcher computes the definitional formula for SS, as finds that = 112. If this is a sample of 20 scores, then what would the value of population variance be using the definitional formula?
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?
7.1 s
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?
7.1 sessions
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?
900
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?
At least 95% of classes were between 68 and 92 decibels.
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 8Sample B: 4, 5, 6, 7, 8, 9, and 10
Both samples have the same standard deviation.
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.
A researcher records the following data: 4, 4, 4, 4, and 3. How would you describe the variability of these data?
It is very small (close to 0) because scores are approximately the same.
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?
Most students drink between 1.5 and 3.1 cups of coffee per study session.
Which of the following is a property of the standard deviation?
Multiplying each score by the same constant will change the standard deviation by that constant.
A researcher records a sample of 30 exam scores and finds that if these data were treated as a population, that the population variance calculation for these data is larger than the sample variance calculation for these same data. Is this outcome for variance possible?
No, the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula.
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
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 30Session B: 8, 10, 12, 16, and 20
Sample A
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 three instruments at the 25th percentile, five instruments at the 50th percentile, and eight instruments at the 75th percentile. What are the IQR and SIQR for these data?
The IQR is 5; the SIQR is 2.5.
How is the sample variance computed differently from the population variance?
The calculation in the denominator is different.
Assuming N does not equal n and all data are otherwise the same, how will the value of the sample variance be different from the population varian
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 SIQR can be defined as ______.
a measure of half the distance between and
A reason for squaring deviations to compute SS in the numerator includes which of the following?
all of these (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 readily by square rooting.)
Which of the following describes the definitional formula for variance?
all of these ( 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.)
Which of the following is consistent with the empirical rule?
all of these (At least 68% of all scores lie within one standard deviation of the mean, At least 95% of all scores lie within two standard deviations of the mean., At least 99.7% of all scores lie within three standard deviations of the mean.)
Which of the following is true about the computational formula for variance?
all of these (The computational formula will always produce the same solution as the definitional formula (give or take rounding errors),. It is a shortcut method for calculating variance when the population or sample size is large., It is derived mathematically from the definitional formula.)
When df are in the denominator, the sample variance is ______.
all of these (an unbiased estimator of the population variance, associated with n - 1 degrees of freedom, computed by dividing SS by df)
The sample variance is computed by dividing SS by ______; whereas the population variance is computed by dividing SS by ______.
df; N
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?
1.0 (9.9 to 8.9)
Regardless of the number of scores in a distribution, the range only includes ______ score(s) in its calculation.
two
A(n) ______ is a sample statistic that equals a population parameter on average
unbiased estimator
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
The sum of the squared deviations of scores from their mean ______.
all of these (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)
The range, a measure of variability, ______.
all of these (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)
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 represent?
df = 23; it represents the number of scores that are free to vary in a sample.
The definitional formula ______ the computational formula for SS
equals
The range of scores between the upper and lower quartiles of a distribution is called the ______.
interquartile range
The variance and standard deviation can never be ______.
negative
Which of the following distributions has the largest variability?
scores: 1, 3, 6, 9, and 12
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
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 18Sample B: 20, 24, 28, 32, and 36
Sample B
0 out of 1 points 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 ______.
at least 89% of children finished their vegetables in 1.2-7.2 min
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 18Sample B: 16, 18, 20, 23, and 26
both samples have the same SD
The advantage of squaring the deviation of each score from the mean and then summing is that ______.
it produces a minimal positive solution that is not zero, as long as all scores are not exactly the same value
Which of the following is an example of a distribution with NO variability?
scores: 5, 5, 5, 5, 5, and 5
An interquartile range removes ______.
the top and bottom 25% of scores in a distribution before calculating range
All other things being equal (so assuming that the value of SS never changes), as sample size increases, ______.
the value of sample variance decreases
A measure of the average squared distance of scores from the mean is called the ______.
variance
Each deviation in the numerator for variance is squared because ______.
without squaring each deviation, the solution for SS would be zero
