Statistics Chapter 4 Gravetter
A population of N = 10 scores has µ = 21 and σ = 3. What is the population variance?
9
For a population, a deviation score is computed as X - σ.
False
In a sample with a mean of M = 4 made up of four scores, two scores are free to vary and the third and fourth scores are fixed.
False
A population of N = 5 scores has a variance of σ2 = 24. If the scores were from a sample, what value would be obtained for the sample variance?
s 2 = 30
A population has µ = 30 and σ = 10. If 5 points are added to every score in the population, what are the new values for the mean and standard deviation?
μ = 35 and σ = 10
A population has SS = 100 and σ2 = 4. What is the value of Σ(X - µ) for the population?
0
A population has SS = 100 and σ 2 = 5. How many scores are in the population?
20
All the possible samples of n = 4 scores are selected from a population with µ = 20. If the average for all of the sample means is calculated, which value will be obtained?
20
In the context of inferential statistics, the sample variance is classified as error variance.
True
A set of 5 scores has SS = 20. If the scores are from a sample, the sample variance is ____. If the scores comprise a population, the population variance is
s 2 = 5; σ2 = 4
In which circumstance is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a population?
when the population mean is not a whole number
A population of scores has µ = 10 and σ = 2. If every score in the population is multiplied by 4, then what are the new values for the mean and standard deviation?
μ = 40 and σ = 8
In order to determine if 10 points below the mean on an exam is an extreme negative score, the _____ needs to be known.
Standard Deviation
A population of N = 5 scores has a mean of µ = 20 and a standard deviation of σ = 4. Which of the following is the correct interpretation of the standard deviation?
The average distance of scores from the mean of μ = 20 is 4 points.
For the following scores, which action will increase the range? Scores: 2, 6, 11, 15
subtract 1 point from the score X = 2
A sample of n = 5 scores has a standard deviation of s = 5. What is the value of SS, the sum of the squared deviations for this sample?
100
In a population of N = 10 scores obtained for a discrete variable for which 0 is not a possible score, the smallest score is X = 8 and the largest is X = 20. What is the range for this population?
12
Compute the interquartile range for the following scores that represent a continuous variable: 1, 2, 2, 2, 4, 5, 10, 12
2
A sample consists of n = 16 scores. How many of the scores are used to calculate the range?
2 scores
A sample of n = 4 scores, has ΣX = 4, and ΣX2 = 32. What is the value of SS for this sample?
28
A sample of n = 15 scores has M = 20 and s2 = 9. What is the sample standard deviation?
3
A population of N = 10 scores has a standard deviation of σ = 2. What is the value of SS, the sum of the squared deviations, for this population?
40
A sample of n = 6 scores has SS = 40. If these same scores were a population, then the SS for the population would be
40
A set of scores ranges from a low of X = 25 to a high of X = 33 and has a mean of 29. Which of the following is the most likely value for the standard deviation for these scores?
5 Points
A positive deviation score indicates that a score in a distribution is less than the mean.
False
After a researcher adds 6 points to every score in a sample, the standard deviation is found to be s = 12. The original sample had a standard deviation of s = 6.
False
After a researcher multiplies every score in a sample by 3, the standard deviation is found to be s = 3. The original sample had a standard deviation of s = 9.
False
For a sample with M = 10 and s = 2, a score of X = 13 would be considered an extreme score, far out in the tail of the distribution
False
For a sample with M = 40 and s = 4, about 70% of the individuals will have scores between X = 32 and X = 48.
False
If a person scores X = 66 on an exam with µ = 70, they scored worse relative to others in the class if σ = 10 than if σ = 5.
False
If the population variance is 6, then the population standard deviation is σ = 36.
False
A researcher conducts a research study to examine how a new treatment for anxiety compares in efficacy to a standard therapy. This researcher assigns clinically anxious participants to either a new treatment or standard treatment for six months, and then observes anxiety levels following. The researcher finds that the new treatment group has an average anxiety score of M = 50 with a standard deviation of s = 5 following treatment, whereas the standard treatment group has an average anxiety score of M = 60 with a standard deviation of s = 6. Which statement below is consistent with how these results would be reported in an APA style journal article?
Clinically anxious individuals who received a new treatment displayed less anxiety levels (M = 50.00, SD = 5.00) than clinically anxious individuals who received a standard treatment (M = 60.00, SD = 6.00).
Because sample variances are computed by dividing SS by n - 1, the average value of the sample variances from all possible random samples consistently _____ the population variance.
Equal
A sample of n = 5 scores has SS = 60 and s2= 15. If the 5 scores were a population, the value of SS would still be 60, but the variance would be σ2 = 10.
False
A sample that was obtained from a continuous variable consists of the following scores: 2, 5, 8, and 9. The range of these scores is 7.
False
It is only appropriate and possible to calculate the variance and standard deviation as measures of variability for variables measured using a(n) _____ scale of measurement.
Interval or ratio
A sample of n = 9 scores has SS = 72. The variance for this sample is s2 = 9
True
A sample with SS = 30 and a variance of s2 = 10 has n = 4 scores
True
A sample with a variance of s2 = 36 has a standard deviation equal to s = 6
True
Data sets can be divided into four quartiles.
True
For a population of scores, the sum of the deviation scores is equal to 0.
True
For a population with µ = 75 and σ = 15, about 95% of the individuals will have scores between X = 45 and X = 105
True
If a person scores X = 80 on an exam with m = 75, they scored worse relative to others in the class if σ = 8 than if σ = 4.
True
If a sample of n = 5 scores has ΣX = 10 and ΣX2 = 100, then SS = 80.
True
In a population with a mean of µ = 30 and a standard deviation of σ= 5, a score of X = 18 would be an extreme value, far out in the tail of the distribution.
True
Multiplying every score in a sample by a constant value will change the value of the standard deviation.
True
If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently _____ the population variance
Underestimate
