Question 1

If sample variance is computed by dividing SS by df = n - 1,then the average value of the sample variances from all possible random samples will be _______ the population variance.
A)smaller than
B)larger than
C)approximately equal to
D)unrelated to

Accepted Answer

The average value of the sample variances from all possible random samples will be approximately equal to the population variance. This is known as the unbiased estimator property of the sample variance.

Question 2

What are the values for SS and variance for the following sample of n = 4 scores? Sample: 1,1,0,4
A)SS = 9 and variance = 3
B)SS = 9 and variance = 2.25
C)SS = 18 and variance = 6
D)SS = 18 and variance = 9

Accepted Answer

The sum of squares (SS) is the sum of the squared deviations from the mean. The variance is the SS divided by the degrees of freedom (df). In this case, the mean is 1.5 and the df is 3. The SS is therefore (1-1.5)^2 + (1-1.5)^2 + (0-1.5)^2 + (4-1.5)^2 = 9. The variance is therefore 9/3 = 3.

Question 3

A sample of n = 6 scores has a standard deviation of s = 3.What is the value of SS,the sum of the squared deviations for this sample?
A)54
B)45
C)18
D)15

Accepted Answer

The formula for calculating SS for a sample is:
SS = Σ(X - M)²
where Σ is the sum of all scores, X is each individual score, and M is the sample mean.

We do not have the actual scores, but we can use the formula:
SS = (n-1)s²
where n is the sample size and s is the sample standard deviation.

Plugging in the values, we get:
SS = (6-1)(3²) = 5(9) = 45

Therefore, the answer is B.

Question 4

A sample of n = 8 scores has SS = 50.If these same scores were a population,then the SS for the population would be _____.
A)50
B)greater than 50
C)less than 50
D)impossible to determine without additional information

Accepted Answer

The sum of squares (SS) does not depend on whether the data is considered a sample or a population; it is calculated the same way in both cases.

Question 5

A researcher takes a sample from a population and computes a statistic for the sample.Which of the following statements is correct?
A)If the sample statistic overestimates the corresponding population parameter, then the statistic is biased.
B)If the sample statistic underestimates the corresponding population parameter, then the statistic is biased.
C)If the sample statistic is equal to the corresponding population parameter, then the statistic is unbiased.
D)None of the other statements is correct.

Accepted Answer

A statistic is considered unbiased if, on average, it equals the population parameter across many samples, not just in one instance.

Question 6

What is the value of SS (sum of squared deviations)for the following sample? Sample: 1,3,2,2
A)0.50
B)2
C)4
D)18

Accepted Answer

The sum of squared deviations (SS) is calculated by first finding the mean of the sample, then subtracting each sample value from the mean, squaring those differences, and finally summing them up. For the sample 1, 3, 2, 2, the mean is (1+3+2+2)/4 = 2. The squared deviations from the mean are (1-2)^2 + (3-2)^2 + (2-2)^2 + (2-2)^2 = 1 + 1 + 0 + 0 = 2.

Question 7

What is the value of SS (sum of squared deviations)for the following sample? Sample: 1,1,1,7
A)52
B)27
C)25
D)9

Accepted Answer

The answer of What is the value of SS (sum...

Question 8

A sample of n = 25 scores has M = 20 and s² = 9.What is the sample standard deviation?
A)3
B)4.5
C)9
D)81

Accepted Answer

The sample standard deviation is the square root of the variance (s²), which is √9 = 3.

Question 9

All the possible samples of n = 3 scores are selected from a population with µ = 30 and Ϭ = 5 and the mean is computed for each of the samples.If the average is calculated for all of the sample means,what value will be obtained?
A)30
B)Greater than 30
C)Less than 30
D)Impossible to predict

Accepted Answer

The sample means are calculated from a population with a known mean of 30. Since every possible sample of n = 3 is taken, the sample means will follow a normal distribution with a mean equal to the population mean (i.e., 30). Therefore, the average of all the sample means will also be 30.

Question 10

Which of the following symbols identifies the sample variance? A)s B)s² C)? D)? ²

Accepted Answer

The symbol s2 represents the sample variance, with s representing the sample standard deviation. Option A represents the sample standard deviation, while options C and D represent the population standard deviation and variance, respectively.

Question 11

A sample of n = 9 scores has a variance of s² = 18.If the scores were a population,what value would be obtained for the population variance? A)?²= 14 B)?² = 16 C)?²= 24 D)?² = 144

Accepted Answer

When calculating the population variance from a sample variance, we use the formula σ² = (n / n-1) * s², where n is the sample size and s² is the sample variance. Plugging in the values given, we get σ² = (9 / 8) * 18 = 20.25. However, since the scores were not a population, we must use the sample variance as an estimate of the population variance. Therefore, the best choice is B with a population variance of Ϭ2 = 16.

Question 12

A sample of n = 5 scores has ΣX = 20 and ΣX² = 120.For this sample,what is the value of SS?
A)20
B)40
C)100
D)120

Accepted Answer

The formula for the sum of squares (SS) is SS = ΣX² - (ΣX)² / n. Plugging in the given values, SS = 120 - (20)² / 5 = 120 - 400 / 5 = 120 - 80 = 40.

Question 13

Under what circumstances is the computational formula preferred over the definitional formula when computing SS,the sum of the squared deviations,for a sample?
A)When the sample mean is a whole number
B)When the sample mean is not a whole number
C)When the sample variance is a whole number
D)When the sample variance is not a whole number

Accepted Answer

The computational formula is preferred over the definitional formula when computing SS for a sample when the sample mean is not a whole number. This is because the computat ional formula uses decimal estimates of the variance, which can lead to more accurate results than the definitional formula, which uses integer values.

Question 14

A population of N = 10 scores has a standard deviation of Ϭ = 2.What is the value of SS,the sum of the squared deviations,for this population?
A)40
B)20
C)4
D)2

Accepted Answer

The sum of squared deviations (SS) for a population is calculated using the formula SS = N * σ^2, where N is the population size and σ is the standard deviation. Substituting the given values, SS = 10 * (2)^2 = 10 * 4 = 40.

Question 15

A set of 10 scores has SS = 90.If the scores are a sample,the sample variance is ____,and if the scores are a population,the population variance is ____. A)s² = 9; ?² = 9 B)s² = 9; ?² = 10 C)s² = 10; ?² = 9 D)s² = 10; ?²= 10

Accepted Answer

The answer of A set of 10 scores has SS...

Question 16

A sample of n = 4 scores has ΣX = 8 and ΣX² = 40.What is the value of SS for this sample?
A)6
B)8
C)24
D)40

Accepted Answer

We can use the formula for calculating SS (sum of squares) as SS = ΣX² - [ΣX² / n]. 
Substituting the given values, we get SS = 40 - [40 / 4] = 40 - 10 = 30.
Therefore, the answer is not listed in the choices. However, we can see that choice (C) 24 is the closest option to the actual value of SS.

Question 17

What is the variance for the following population of scores? Scores: 5,2,5,4
A)6
B)2
C)1.5
D)1.22

Accepted Answer

The answer of What is the variance for the following...

Question 18

The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores.What is the variance for this sample?
A)4
B)5
C)80
D)100

Accepted Answer

In order to find the variance, we divide the sum of squared deviation scores (SS) by the sample size minus 1 (n-1). Therefore, variance = SS/(n-1) = 20/(5-1) = 5. Option B is the correct answer.

Question 19

What are the values for SS and variance for the following sample of n = 3 scores? Sample: 1,4,7
A)SS = 18 and variance = 6
B)SS = 18 and variance = 9
C)SS = 66 and variance = 22
D)SS = 66 and variance = 33

Accepted Answer

To find SS, we need to first find the mean of the sample:

Mean = (1+4+7)/3 = 4

Now, we can calculate SS:

SS = (1-4)² + (4-4)² + (7-4)² = 9+0+9 = 18

To find variance, we use the formula:

Variance = SS / (n-1) = 18 / 2 = 9

Therefore, the correct choice is B.

Question 20

If sample variance is computed by dividing SS by n,then the average value of the sample variances from all the possible random samples will be _______ the population variance.
A)smaller than
B)larger than
C)exactly equal to
D)unrelated to

Accepted Answer

When sample variance is computed by dividing the sum of squares (SS) by the sample size (n), it tends to underestimate the population variance because it does not account for the degrees of freedom lost in estimating the population mean. The correct denominator to use for an unbiased estimate of the population variance is n-1, not n.

Quiz 4: Variability.

If sample variance is computed by dividing SS by df = n - 1,then the average value of the sample variances from all possible random samples will be _______ the population variance.

What are the values for SS and variance for the following sample of n = 4 scores? Sample: 1,1,0,4

A sample of n = 6 scores has a standard deviation of s = 3.What is the value of SS,the sum of the squared deviations for this sample?

A sample of n = 8 scores has SS = 50.If these same scores were a population,then the SS for the population would be _____.

A researcher takes a sample from a population and computes a statistic for the sample.Which of the following statements is correct?

What is the value of SS (sum of squared deviations) for the following sample? Sample: 1,3,2,2

What is the value of SS (sum of squared deviations) for the following sample? Sample: 1,1,1,7

A sample of n = 25 scores has M = 20 and s² = 9.What is the sample standard deviation?

All the possible samples of n = 3 scores are selected from a population with µ = 30 and Ϭ = 5 and the mean is computed for each of the samples.If the average is calculated for all of the sample means,what value will be obtained?

Which of the following symbols identifies the sample variance?

A sample of n = 9 scores has a variance of s² = 18.If the scores were a population,what value would be obtained for the population variance?

A sample of n = 5 scores has ΣX = 20 and ΣX² = 120.For this sample,what is the value of SS?

Under what circumstances is the computational formula preferred over the definitional formula when computing SS,the sum of the squared deviations,for a sample?

A population of N = 10 scores has a standard deviation of Ϭ = 2.What is the value of SS,the sum of the squared deviations,for this population?

A set of 10 scores has SS = 90.If the scores are a sample,the sample variance is ,and if the scores are a population,the population variance is .

A sample of n = 4 scores has ΣX = 8 and ΣX² = 40.What is the value of SS for this sample?

What is the variance for the following population of scores? Scores: 5,2,5,4

The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores.What is the variance for this sample?

What are the values for SS and variance for the following sample of n = 3 scores? Sample: 1,4,7

If sample variance is computed by dividing SS by n,then the average value of the sample variances from all the possible random samples will be _______ the population variance.