Question 1

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the expected value for the distribution of sample means?
A)6
B)18
C)80/3
D)80

Accepted Answer

The expected value of the distribution of sample means for a sample size of n is equal to the population mean. Therefore, the expected value in this scenario is equal to μ = 80. Choice D is the correct answer.

Question 2

What symbol is used to identify the standard error of M?
A)σM
B)µ
C)σ
D)MM

Accepted Answer

The symbol σM is commonly used to represent the standard error of the mean (M).

Question 3

What is the expected value of M?
A)The sample mean
B)The sample standard deviation
C)The mean of the distribution of sample means
D)The standard deviation of the distribution of sample means

Accepted Answer

The expected value of M is the mean of the distribution of sample means, which is represented by μ (mu). This is because the mean of the sample means is the best estimate of the population mean. A) The sample mean is only appropriate for describing a single sample. B) The sample standard deviation is a measure of the variability within a single sample, not across multiple samples. D) The standard deviation of the distribution of sample means is also important, but not the expected value.

Question 4

If random samples,each with n = 9 scores,are selected from a normal population with µ = 80 and σ = 18,how much difference,on average,should there be between a sample mean and the population mean?
A)2 points
B)3 points
C)6 points
D)18 points

Accepted Answer

The answer of If random samples,each with n = 9...

Question 5

A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8,and the sample mean is M = 43.What is the expected value for the sample mean?
A)40
B)10
C)8
D)2

Accepted Answer

The expected value for the sample mean is equal to the population mean, which is given as μ = 40. Therefore, the expected value for the sample mean is also 40.

Question 6

A random sample of n = 60 scores is selected from a population.Which of the following distributions will definitely be normal?
A)The scores in the sample will definitely form a normal distribution.
B)The scores in the population definitely will form a normal distribution.
C)The distribution of sample means will definitely form a normal distribution.
D)None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.

Accepted Answer

According to the Central Limit Theorem, the distribution of sample means will approach a normal distribution as the sample size increases, regardless of the distribution of the population from which the sample is drawn. Therefore, the distribution of sample means will definitely be normal for a sample size of 60 or more.

Question 7

If random samples,each with n = 9 scores,are selected from a normal population with µ = 80 and σ = 36,what is the expected value for the distribution of sample means?
A)4
B)12
C)16
D)80

Accepted Answer

The expected value of the distribution of sample means is equal to the population mean, which is 80.

Question 8

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the standard error for the distribution of sample means?
A)80
B)18
C)6
D)2

Accepted Answer

The formula for standard error of the mean is:

SE = σ/√n

Plugging in the values given:

SE = 18/√9 = 6

Therefore, the standard error for the distribution of sample means is 6.

Question 9

For a population with µ = 80 and σ = 20,the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ____.
A)5; 80
B)80; 5
C)20; 20
D)80; 1.25

Accepted Answer

The expected value of the distribution of sample means (also known as the mean of the sampling distribution) is equal to the population mean, so it is 80. The standard error of the distribution of sample means is equal to the population standard deviation divided by the square root of the sample size, which is 20/sqrt(16) = 5. Therefore, the correct answer is B.

Question 10

Samples of n = 16 scores are selected from a population.If the distribution of sample means has an expected value of 40 and a standard error of 2,what is the mean and the standard deviation for the population?
A)µ = 40 and σ = 2
B)µ = 40 and σ = 8
C)µ = 40 and σ = 32
D)µ = 160 and σ = 2

Accepted Answer

The mean of the distribution of sample means is equal to the mean of the population, which is given as 40. 
The standard deviation of the distribution of sample means (standard error) is equal to the standard deviation of the population divided by the square root of the sample size. Therefore, 
2 = σ / sqrt(16) 
2 = σ / 4 
σ = 8 
Therefore, the correct answer is B, with a mean of 40 and a standard deviation of 8 for the population.

Question 11

A random sample of n = 6 scores is selected from a population.Which of the following distributions will definitely be normal?
A)The scores in the sample will definitely form a normal distribution.
B)The scores in the population will definitely form a normal distribution.
C)The distribution of sample means will definitely form a normal distribution.
D)None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.

Accepted Answer

The normality of the distributions of the sample, population, or distribution of sample means cannot be guaranteed without further information about the population distribution or the sample size in relation to the central limit theorem.

Question 12

For a particular population,a sample of n = 4 scores has a standard error of 6.For the same population,a sample of n = 16 scores would have a standard error of _____.
A)8
B)6
C)3
D)2

Accepted Answer

The standard error of the mean decreases as the sample size increases, inversely proportional to the square root of the sample size (n). Since the sample size increases from 4 to 16 (which is a factor of 4), the standard error decreases by a factor of 2 (the square root of 4), making the new standard error 3 (6 divided by 2).

Question 13

What is the standard error of M?
A)The sample mean
B)The sample standard deviation
C)The mean of the distribution of sample means
D)The standard deviation of the distribution of sample means

Accepted Answer

The standard error of M quantifies the variability of the sample means expected from random sampling. It is calculated as the standard deviation of the distribution of sample means, which is a theoretical distribution that describes the possible sample means that can be obtained from a certain population. Thus, option D is the correct choice. The sample mean (option A) is just the arithmetic average of a particular sample, while the sample standard deviation (option B) describes the variability within that sample. The mean of the distribution of sample means (option C) is a theoretical value that does not take into account the variability among samples.

Question 14

For a particular population,a sample of n = 4 scores has an expected value of 10.For the same population,a sample of n = 25 scores would have an expected value of _____.
A)4
B)8
C)10
D)20

Accepted Answer

The expected value of a sample does not depend on the sample size but rather on the population parameters. Therefore, regardless of the sample size, if the population has an expected value of 10, then any sample drawn from that population should also have an expected value of 10.

Question 15

Under what circumstances will the distribution of sample means be normal?
A)It is always normal
B)Only if the population distribution is normal
C)Only if the sample size is greater than 30
D)If the population is normal or if the sample size is greater than 30

Accepted Answer

The distribution of sample means will be normal if either the population distribution is normal or if the sample size is greater than 30. Therefore, choice D is the correct answer.

Question 16

A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8,and the sample mean is M = 43.What is the standard error for the sample mean?
A)8
B)4
C)3
D)2

Accepted Answer

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

Question 17

A sample of n = 16 scores is selected from a population with μ = 80 with σ = 20.On average,how much error would be expected between the sample mean and the population mean?
A)20 points
B)5 points
C)4 points
D)1.25 points

Accepted Answer

The standard error of the mean (SEM) can be calculated as σ/√n. In this case, SEM = 20/√16 = 5. This means that we would expect the sample mean to differ from the population mean by about 5 points on average. Therefore, the best choice is B) 5 points.

Question 18

A sample of n = 100 scores is selected from a population with μ = 80 with σ = 20.On average,how much error is expected between the sample mean and the population mean?
A)0.2 points
B)0.8 points
C)2 points
D)4 points

Accepted Answer

The standard error of the mean (SEM) can be calculated using the formula SEM = σ/√n. Plugging in the given values, we get SEM = 20/√100 = 2. This means that on average, we can expect an error of 2 points between the sample mean and the population mean. Therefore, the best choice is C) 2 points.

Question 19

If random samples,each with n = 4 scores,are selected from a normal population with µ = 80 and σ = 36,what is the standard error for the distribution of sample means?
A)4
B)9
C)18
D)36

Accepted Answer

The formula for standard error is: 
standard error = standard deviation of population / square root of sample size.

Here, we have:
standard deviation of population (σ) = 36 
sample size (n) = 4

So, the standard error = 36 / sqrt(4) = 36 / 2 = 18.

Therefore, the best choice is C, with the standard error being 18.

Question 20

If all the possible random samples with n = 36 scores are selected from a normal population with µ = 80 and σ = 18,and the mean is calculated for each sample,what is the average of all the sample means?
A)2
B)6
C)80
D)Cannot be determined without additional information

Accepted Answer

According to the Central Limit Theorem, the distribution of sample means will be normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, the average of all possible sample means will be equal to the population mean, which is 80.

Quiz 7: Probability and Samples: The Distribution of Sample Means.

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the expected value for the distribution of sample means?

What symbol is used to identify the standard error of M?

What is the expected value of M?

If random samples,each with n = 9 scores,are selected from a normal population with µ = 80 and σ = 18,how much difference,on average,should there be between a sample mean and the population mean?

A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8,and the sample mean is M = 43.What is the expected value for the sample mean?

A random sample of n = 60 scores is selected from a population.Which of the following distributions will definitely be normal?

If random samples,each with n = 9 scores,are selected from a normal population with µ = 80 and σ = 36,what is the expected value for the distribution of sample means?

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the standard error for the distribution of sample means?

For a population with µ = 80 and σ = 20,the distribution of sample means based on n = 16 will have an expected value of and a standard error of .

Samples of n = 16 scores are selected from a population.If the distribution of sample means has an expected value of 40 and a standard error of 2,what is the mean and the standard deviation for the population?

A random sample of n = 6 scores is selected from a population.Which of the following distributions will definitely be normal?

For a particular population,a sample of n = 4 scores has a standard error of 6.For the same population,a sample of n = 16 scores would have a standard error of _____.

What is the standard error of M?

For a particular population,a sample of n = 4 scores has an expected value of 10.For the same population,a sample of n = 25 scores would have an expected value of _____.

Under what circumstances will the distribution of sample means be normal?

A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8,and the sample mean is M = 43.What is the standard error for the sample mean?

A sample of n = 16 scores is selected from a population with μ = 80 with σ = 20.On average,how much error would be expected between the sample mean and the population mean?

A sample of n = 100 scores is selected from a population with μ = 80 with σ = 20.On average,how much error is expected between the sample mean and the population mean?

If random samples,each with n = 4 scores,are selected from a normal population with µ = 80 and σ = 36,what is the standard error for the distribution of sample means?

If all the possible random samples with n = 36 scores are selected from a normal population with µ = 80 and σ = 18,and the mean is calculated for each sample,what is the average of all the sample means?