Question 1

You have a score of X = 65 on a math exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the most favorable position within the class?​

Accepted Answer

A larger standard deviation means scores are more spread out, so a score of 65 would be less below average compared to a smaller standard deviation.

Question 2

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

Accepted Answer

To find SS, we need to calculate the deviation of each score from the mean, square each deviation, and then sum up the squared deviations.

The mean of the sample is (1 + 1 + 1 + 3) / 4 = 1.5.

The deviations from the mean are:

-0.5, -0.5, -0.5, 1.5

Squaring each deviation gives:

0.25, 0.25, 0.25, 2.25

Summing up the squared deviations gives:

0.25 + 0.25 + 0.25 + 2.25 = 3

Therefore, the value of SS for this sample is 3. Choice C is the correct answer.

Question 3

A sample of n = 5 scores has ΣX = 20 and ΣX² = 180.For this sample,what is the value of the sample standard deviation,s?

Accepted Answer

The sample standard deviation, $s$, is calculated using the formula $s = \sqrt{\frac{\Sigma X^2 - (\Sigma X)^2 / n}{n - 1}}$. Given $\Sigma X = 20$, $\Sigma X^2 = 180$, and $n = 5$, we substitute these values into the formula: $s = \sqrt{\frac{180 - (20)^2 / 5}{5 - 1}} = \sqrt{\frac{180 - 80}{4}} = \sqrt{\frac{100}{4}} = \sqrt{25} = 5$.

Question 4

Which of the following is true for most distributions?​

Accepted Answer

The Empirical Rule states that for a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean. While most distributions are not perfectly normal, they often follow a similar pattern, making choice C the best option.

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 the____.​

Accepted Answer

The standard deviation is a measure of the spread of scores around the mean. Since the range of scores is from 5 to 10, the standard deviation must be smaller than the range, which is 5.

Question 6

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?​

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 7

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

Accepted Answer

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

Question 8

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.​

Accepted Answer

When calculating the sample variance by dividing the sum of squares (SS) by n, this results in a biased estimate of the population variance. This means that on average, the sample variances from all possible random samples will be smaller than the population variance. To obtain an unbiased estimate of the population variance, one should divide the sum of squares by n-1 instead.

Question 9

Which set of scores has the smallest standard deviation?​

Accepted Answer

The set of scores in option C has the smallest range of values (only a difference of 4 between the highest and lowest score), indicating that the scores are more tightly clustered around the mean. This results in a smaller standard deviation.

Question 10

There is a six-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.​

Accepted Answer

A smaller variance (2 in this case) means the distributions are tighter, making the difference between the means more visually distinct in a graph.

Question 11

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.​

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 12

For a particular sample of size n=10,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 will be ____.​

Accepted Answer

Since the largest deviation is 11 and the smallest is 4, we know that the range is 11-4=7. The standard deviation measures the average deviation of the scores from the mean, so it must fall somewhere between the largest deviation of 11 and the smallest deviation of 4. Therefore, the standard deviation must be between 4 and 11.

Question 13

A sample of n = 4 scores has ΣX = 8 and ΣX² = 40.What is the value of the sample variance,s²?

Accepted Answer

The answer of A sample of n = 4 scores...

Question 14

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?​

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 15

For a sample of n = 16 scores,how many scores are used to calculate the sample variance?​

Accepted Answer

The formula for sample variance involves using all the scores in the sample, so all 16 scores would be used to calculate the sample variance. Therefore, the answer is D.

Question 16

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 ____.​

Accepted Answer

The sample variance can be calculated as SS/(n-1) where SS is the sum of squared deviations from the mean, and n is the sample size. In this case, SS = 90 and n = 10, so the sample variance is 90/(10-1) = 10.

If the scores are a population, the population variance can be calculated as SS/n, where SS is the sum of squared deviations from the mean, and n is the population size. Since we don't know the population size, we can't calculate the population variance exactly. However, we can make an estimate based on the sample variance. If the sample is representative of the population, we can assume that the sample variance is a good estimate of the population variance. In that case, the population variance would also be 10.

Therefore, the best choice is C, which has matching sample and population variances of 10.

Question 17

Given a population with mean m = 60,which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?​

Accepted Answer

A smaller standard deviation (σ = 2) means that the scores are more closely clustered around the mean, making a score of 68 more extreme compared to larger standard deviations.

Question 18

What is the value of SS (sum of squared deviations)for the following sample? Sample: 2,3,4,7​

Accepted Answer

The sum of squared deviations (SS) is calculated by first finding the mean of the sample, then subtracting the mean from each value in the sample, squaring those differences, and finally summing them up. For the sample 2, 3, 4, 7, the mean is (2+3+4+7)/4 = 16/4 = 4. The squared deviations from the mean are (2-4)^2 + (3-4)^2 + (4-4)^2 + (7-4)^2 = 4 + 1 + 0 + 9 = 14.

Question 19

You have a score of X = 75 on a statistics exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the highest position within the class?​

Accepted Answer

A lower standard deviation (σ = 1) indicates that the scores are more closely clustered around the mean. With a score of 75 and a mean of 70, a lower standard deviation means your score is farther from the mean relative to most other scores, placing you higher within the class distribution.

Question 20

Which of the following symbols identifies the sample variance?​

Accepted Answer

The symbol $s^2$ is used to represent the sample variance, which is the correct choice here.

Quiz 4: Variability

You have a score of X = 65 on a math exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the most favorable position within the class?

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

A sample of n = 5 scores has ΣX = 20 and ΣX² = 180.For this sample,what is the value of the sample standard deviation,s?

Which of the following is true for most distributions?

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

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

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.

Which set of scores has the smallest standard deviation?

There is a six-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.

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 of size n=10,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 will be ____.

A sample of n = 4 scores has ΣX = 8 and ΣX² = 40.What is the value of the sample variance,s²?

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?

For a sample of n = 16 scores,how many scores are used to calculate the sample variance?

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 .

Given a population with mean m = 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 is the value of SS (sum of squared deviations) for the following sample? Sample: 2,3,4,7

You have a score of X = 75 on a statistics exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the highest position within the class?

Which of the following symbols identifies the sample variance?

Quiz 4: Variability

You have a score of X = 65 on a math exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the most favorable position within the class?​

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

A sample of n = 5 scores has ΣX = 20 and ΣX2 = 180.For this sample,what is the value of the sample standard deviation,s?​

Which of the following is true for most distributions?​

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

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

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.​

Which set of scores has the smallest standard deviation?​

There is a six-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.​

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 of size n=10,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 will be ____.​

A sample of n = 4 scores has ΣX = 8 and ΣX2 = 40.What is the value of the sample variance,s2?​

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?​

For a sample of n = 16 scores,how many scores are used to calculate the sample variance?​

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 ____.​

Given a population with mean m = 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 is the value of SS (sum of squared deviations) for the following sample? Sample: 2,3,4,7​

You have a score of X = 75 on a statistics exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the highest position within the class?​

Which of the following symbols identifies the sample variance?​

You have a score of X = 65 on a math exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the most favorable position within the class?

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

A sample of n = 5 scores has ΣX = 20 and ΣX² = 180.For this sample,what is the value of the sample standard deviation,s?

Which of the following is true for most distributions?

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

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

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.

Which set of scores has the smallest standard deviation?

There is a six-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.

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 of size n=10,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 will be ____.

A sample of n = 4 scores has ΣX = 8 and ΣX² = 40.What is the value of the sample variance,s²?

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?

For a sample of n = 16 scores,how many scores are used to calculate the sample variance?

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 .

Given a population with mean m = 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 is the value of SS (sum of squared deviations) for the following sample? Sample: 2,3,4,7

You have a score of X = 75 on a statistics exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the highest position within the class?

Which of the following symbols identifies the sample variance?