Question 1

Which of the following describes the definitional formula for variance?

Accepted Answer

A)  It is stated in terms of how variance is defined.
B)  It is computed using SS in the numerator.
C)  It is a measure of the average squared distance that scores deviate from their mean.
D)  all of the above D

Question 2

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

Accepted Answer

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

Question 3

Suppose a researcher selects a sample of 19 participants and computes SS = 162.In this example,the standard deviation is 3.

Accepted Answer

A) True 
 B)False  True

Question 4

The degrees of freedom for the sample variance

Accepted Answer

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

Question 5

Suppose a researcher observes a population of 25 people and computes SS = 360.In this example,the variance is 15.

Accepted Answer

A) True 
 B)False

Question 6

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?

Accepted Answer

A)  36
B)  150
C)  900
D)  There is not enough information to answer this question.

Question 7

Suppose a researcher selects a sample of 16 participants and computes SS = 60.In this example,the standard deviation is 4.

Accepted Answer

A) True 
 B)False

Question 8

The standard deviation is always positive or equal to 0.

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

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

Question 10

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?

Accepted Answer

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.

Question 11

A researcher records a sample of 30 exam scores and finds that the population mean for these data is larger than the sample variance.Is this possible?

Accepted Answer

A)  yes,the population variance is usually larger than the sample variance
B)  no,the population variance will only be larger when at least 50 scores are recorded
C)  no,the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula
D)  not possible to know because the scores are not given

Question 12

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

Accepted Answer

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

Question 13

For nonnormal distributions,99.7% of data will fall within three standard deviations of the mean.

Accepted Answer

A) True 
 B)False

Question 14

The population standard deviation is equal to 10 when SS = 100 and n = 10.

Accepted Answer

A) True 
 B)False

Question 15

If all scores in a distribution are negative values,then the standard deviation will also be a negative value.

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

A)  68% of children finished their vegetables in 3.2 to 5.2 minutes.
B)  50% of children finished their vegetables in at least 3.2 minutes.
C)  99.7% of children finished their vegetables in 2.2 to 6.2 minutes.
D)  At least 89% of children finished their vegetables in 1.2 to 7.2 minutes.

Question 17

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

Accepted Answer

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

Question 18

The degrees of freedom for sample variance is equal to N.

Accepted Answer

A) True 
 B)False

Question 19

The advantage of squaring the deviation of each score from the mean and then summing is that

Accepted Answer

A)  it makes the sample variance an unbiased estimator of the population variance
B)  it makes the degrees of freedom for sample variance equal to n - 1
C)  it produces a minimal positive solution that is not zero,so long as all scores are not exactly the same value
D)  both A and C

Question 20

The standard deviation is typically reported in research reports with the mean for a data set.

Accepted Answer

A) True 
 B)False

Exam 4: Summarizing Data: Variability

Which of the following describes the definitional formula for variance?

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

Suppose a researcher selects a sample of 19 participants and computes SS = 162.In this example,the standard deviation is 3.

The degrees of freedom for the sample variance

Suppose a researcher observes a population of 25 people and computes SS = 360.In this example,the variance is 15.

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?

Suppose a researcher selects a sample of 16 participants and computes SS = 60.In this example,the standard deviation is 4.

The standard deviation is always positive or equal to 0.

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 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 researcher records a sample of 30 exam scores and finds that the population mean for these data is larger than the sample variance.Is this possible?

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

For nonnormal distributions,99.7% of data will fall within three standard deviations of the mean.

The population standard deviation is equal to 10 when SS = 100 and n = 10.

If all scores in a distribution are negative values,then the standard deviation will also be a negative value.

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

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 is equal to N.

The advantage of squaring the deviation of each score from the mean and then summing is that

The standard deviation is typically reported in research reports with the mean for a data set.