Question 1

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

The average value of the sample variances from all possible random samples will be smaller than the population variance. This is due to the fact that the denominator of the sample variance formula is n-1, which results in an upward bias in the estimate of the population variance. As such, the sample variance tends to be smaller than the population variance, and the average of sample variances from all possible random samples will be even smaller.

Question 2

There is a 6-point difference between two sample means.If the two samples have the same variance, then which of the following values for the variance would make the mean difference easiest to see in a graph showing the two distributions. A)s² = 2 B)s² = 8 C)s² = 16 D)s² = 64

Accepted Answer

A smaller variance means the data points are closer to the mean, making the difference between the two means more pronounced and easier to see in a graph.

Question 3

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 answer of What are the values for SS and...

Question 4

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)$\sigma$² = 14 B)$\sigma$² = 16 C)$\sigma$² = 24 D)$\sigma$² = 144

Accepted Answer

The answer of A sample of n = 9 scores...

Question 5

The smallest score in a population is X = 5 and the largest score is X = 10.Based on this information, you can conclude that ______.
A)the population mean is somewhere between 5 and 10.
B)the population standard deviation is smaller than 6.
C)the population mean is between 5 and 10, and the standard deviation is less than 6.
D)None of the other choices is correct.

Accepted Answer

The mean must be between the smallest and largest scores, so it is between 5 and 10. The standard deviation, which measures spread, cannot exceed the range (10-5=5), so it is less than 6.

Question 6

On an exam with a mean of μ = 70, you have a score of X = 75.Which of the following values for the standard deviation would give you the highest position within the class?
A)σ = 1
B)σ = 5
C)σ = 10
D)cannot determine from the information given

Accepted Answer

A smaller standard deviation indicates that scores are closer to the mean. With σ = 1, your score of 75 is 5 standard deviations above the mean, giving you the highest relative position compared to larger standard deviations.

Question 7

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

Accepted Answer

The variance for a population is calculated by dividing the sum of squared deviations (SS) by the number of scores (N). Thus, variance = SS / N = 20 / 5 = 4.

Question 8

Which of the following is true for most distributions?
A)Around 30% of the scores will be located within one standard deviation of the mean.
B)Around 50% of the scores will be located within one standard deviation of the mean.
C)Around 70% of the scores will be located within one standard deviation of the mean.
D)Around 90% of the scores will be located within one standard deviation of the mean.

Accepted Answer

This is known as the 68-95-99.7 rule, where approximately 68% of the scores will fall within one standard deviation of the mean. This is true for most, but not all, distributions.

Question 9

What is the value of SS for the following set of scores? Scores: 0, 1, 4, 5
A)17
B)18
C)42
D)Cannot answer without knowing whether it is a sample or a population.

Accepted Answer

The value of SS (Sum of Squares) can be calculated regardless of whether the data represents a sample or a population. SS = Σ(X - M)^2, where X is each score and M is the mean of the scores. The mean (M) of the scores 0, 1, 4, 5 is (0+1+4+5)/4 = 2.5. SS = (0-2.5)^2 + (1-2.5)^2 + (4-2.5)^2 + (5-2.5)^2 = 6.25 + 2.25 + 2.25 + 6.25 = 17.

Question 10

On an exam with a mean of μ = 70, you have a score of X = 65.Which of the following values for the standard deviation would give you the highest position within the class?
A)σ = 1
B)σ = 5
C)σ = 10
D)cannot determine from the information given

Accepted Answer

A larger standard deviation indicates more variability in scores. With a score below the mean, a larger standard deviation (σ = 10) would place you relatively higher compared to others, as more scores would be spread out below and above the mean.

Question 11

A population has µ = 50 and σ = 5.If 10 points are added to every score in the population, then what are the new values for the mean and standard deviation?
A)µ = 50 and σ = 5
B)µ = 50 and σ = 15
C)µ = 60 and σ = 5
D)µ = 60 and σ = 15

Accepted Answer

Adding 10 to every score in the population will shift both the mean and standard deviation by 10 units. Therefore, the new mean will be µ + 10 = 50 + 10 = 60. However, the standard deviation will remain the same because adding a constant to every score does not change the variability in the data, so σ = 5 remains unchanged. Therefore, the correct answer is C, µ = 60 and σ = 5.

Question 12

A sample of n = 8 scores has SS = 50.If these same scores were a population, then the SS value 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) is calculated the same way for both a sample and a population, so the SS value remains 50.

Question 13

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

Variance is calculated by dividing the sum of squared deviations by n-1 (the number of degrees of freedom). Therefore, variance = SS/(n-1) = 20/(5-1) = 5. Thus, the answer is B.

Question 14

A population of scores has µ = 50 and σ = 5.If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?
A)µ = 50 and σ = 5
B)µ = 50 and σ = 15
C)µ = 150 and σ = 5
D)µ = 150 and σ = 15

Accepted Answer

When every score in a population is multiplied by a constant, the mean (µ) is also multiplied by that constant, and the standard deviation (σ) is multiplied by the absolute value of that constant. Therefore, the new mean is 3*50 = 150, and the new standard deviation is 3*5 = 15.

Question 15

For a population with $\mu$ = 60, which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?
A)? = 1
B)? = 2
C)? = 3
D)? = 4

Accepted Answer

A smaller standard deviation indicates that the data points are closer to the mean. Therefore, with a standard deviation of 1, X = 68 is 8 standard deviations away from the mean, making it the most extreme position.

Question 16

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
 
Next, we calculate the deviation of each score from the mean:
 
Deviation1 = 1 - 4 = -3
Deviation2 = 4 - 4 = 0
Deviation3 = 7 - 4 = 3
 
To find SS, we square each deviation and sum the results:
 
SS = (-3)2 + 02 + 32 = 9 + 0 + 9 = 18
 
Finally, we find the variance by dividing SS by n - 1:
 
variance = SS ÷ (n - 1) = 18 ÷ 2 = 9

Question 17

Which set of scores has the smallest standard deviation?
A)11, 17, 31, 53
B)5, 11, 42, 22
C)145, 143, 145, 147
D)27, 105, 10, 80

Accepted Answer

The set of scores {145, 143, 145, 147} has the smallest standard deviation, as all the scores are very close to each other. This means that there is not much variation within the set, resulting in a smaller standard deviation.

Question 18

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 19

If sample variance is computed by dividing SS by df = n - 1, 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

The average value of the sample variances from all possible random samples, when computed by dividing the sum of squares (SS) by the degrees of freedom (df = n - 1), will be exactly equal to the population variance. This method ensures an unbiased estimate of the population variance.

Question 20

For a particular sample, the largest distance (deviation) between a score and the mean is 11 points.The smallest distance between a score and the mean is 4 points.Therefore, the standard deviation _____.
A)will be less than 4
B)will be between 4 and 11
C)will be greater than 11
D)It is impossible to say anything about the standard deviation.

Accepted Answer

The standard deviation is a measure of the average distance of scores from the mean. Since the largest deviation is 11 and the smallest is 4, the standard deviation will be between these values, as it represents an average of all deviations.

Quiz 4: Variability

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.

There is a 6-point difference between two sample means.If the two samples have the same variance, then which of the following values for the variance would make the mean difference easiest to see in a graph showing the two distributions.

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

The smallest score in a population is X = 5 and the largest score is X = 10.Based on this information, you can conclude that ______.

On an exam with a mean of μ = 70, you have a score of X = 75.Which of the following values for the standard deviation would give you the highest position within the class?

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

Which of the following is true for most distributions?

What is the value of SS for the following set of scores? Scores: 0, 1, 4, 5

On an exam with a mean of μ = 70, you have a score of X = 65.Which of the following values for the standard deviation would give you the highest position within the class?

A population has µ = 50 and σ = 5.If 10 points are added to every score in the population, then what are the new values for the mean and standard deviation?

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

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 population of scores has µ = 50 and σ = 5.If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?

For a population with μ\muμ = 60, which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?

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

Which set of scores has the smallest standard deviation?

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

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

For a particular sample, the largest distance (deviation) between a score and the mean is 11 points.The smallest distance between a score and the mean is 4 points.Therefore, the standard deviation _____.

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.

For a population with $\mu$ = 60, which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?