Question 1

What happens to the standard error of M as sample size increases?​
A)It also increases.​
B)​It decreases.
C)​It stays constant.
D)​The standard error does not change in a predictable manner when sample size increases.

Accepted Answer

The standard error of the mean (M) decreases as sample size increases. This is due to the fact that a larger sample size reduces the variability of the sample means, making the mean estimate more precise and closer to the true population mean.

Question 2

The distribution of sample means ____.​
A)​is always a normal distribution
B)​will be normal only if the population distribution is normal
C)​will be normal only if the sample size is at least n = 30
D)​will be normal if either the population is normal or the sample size is n > 30

Accepted Answer

The distribution of sample means will be approximately normal if the population from which the samples are drawn is normally distributed, regardless of the sample size. This is also true if the population is not normally distributed but the sample size is large (usually n > 30), according to the Central Limit Theorem.

Question 3

What happens to the expected value of M as sample size increases?​
A)​It also increases.
B)​It decreases.
C)​It stays constant.
D)​The expected value does not change in a predictable manner when sample size increases.

Accepted Answer

The expected value of a statistic (like the mean, M) is a theoretical value based on the population from which samples are drawn. It does not change with the size of the sample because it is a property of the population.

Question 4

What term is used to identify the standard deviation of the distribution of sample means?​
A)the expected value of M​
B)​the standard error of M
C)​the sample mean
D)​the central limit mean

Accepted Answer

The term used to identify the standard deviation of the distribution of sample means is the standard error of M.

Question 5

What term is used to identify the mean of the distribution of sample means?​
A)​the expected value of M
B)​the standard error of M
C)​the sample mean
D)​the central limit mean

Accepted Answer

The term used to identify the mean of the distribution of sample means is the expected value of M. This is because the expected value of the sample means is equal to the population mean, which is the parameter that we are interested in estimating. Therefore, the expected value of M is an important statistic in inferential statistics.

Question 6

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18.What is the expected value of M,the mean of 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 is equal to the population mean, which is 80 in this case. Therefore, the correct answer is D) 80.

Question 7

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 expected error between the sample mean and the population mean can be calculated using the standard error of the mean formula, which is σ/√n. Here, σ = 20 and n = 16. So, the standard error = 20/√16 = 20/4 = 5 points. This indicates, on average, how much the sample mean is expected to deviate from the population mean.

Question 8

A random sample of n = 36 scores is selected from a population.Which of the following distributions will definitively be normal?​
A)​The scores in the sample will form a normal distribution.
B)​The scores in the population will form a normal distribution.
C)​The distribution of sample means will form a normal distribution.
D)​None of the distributions - the sample, the population, the 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 if the sample size is large enough (typically n ≥ 30). The other options do not definitively guarantee a normal distribution.

Question 9

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 by dividing the population standard deviation by the square root of the sample size. In this case, the SEM would be 20/√100 = 2. This means that we would expect, on average, a difference of 2 points between the sample mean and the population mean. Therefore, the best choice is C) 2 points.

Question 10

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,then what is the average of all the sample means?​
A)​2
B)​6
C)​80
D)​It cannot be determined without additional information.

Accepted Answer

The average of all the sample means is equal to the population mean, which is given as µ=80. Thus the answer is C.

Question 11

A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively be normal?​
A)​The scores in the sample will form a normal distribution.
B)​The scores in the population will form a normal distribution.
C)​The distribution of sample means will form a normal distribution.
D)​None of the distributions - the sample, the population, the distribution of sample means -will definitely be normal.

Accepted Answer

The normality of the distributions cannot be definitively determined without knowing the distribution of the population. A sample size of n = 4 is too small to ensure the distribution of sample means is normal unless the population distribution is known to be normal.

Question 12

Under what circumstances is distribution of sample means normal?​
A)It is always normal​
B)​Only if the population distribution is normal
C)​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 is normal if either the population is normal or the sample size is greater than 30 due to the Central Limit Theorem. Therefore, choice D is the best answer.

Question 13

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

Accepted Answer

The expected value of the mean of the distribution of sample means is equal to the population mean, which is 80. This is because the sample means will tend to cluster around the population mean due to the central limit theorem. Therefore, the best choice is D.

Question 14

If random samples,each with n = 36 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 standard error of the mean (SEM) can be calculated using the formula σ/√n, where σ is the population standard deviation and n is the sample size. In this case, the SEM is 18/√36 = 3. Therefore, we can expect that on average, a sample mean will differ from the population mean by about 3 points. This is because the sample mean is an estimate of the population mean and will likely differ to some extent due to random sampling error. The larger the sample size, the smaller the SEM and the closer the sample mean will be to the population mean.

Question 15

For a particular population,a sample of n = 9 scores has a standard error of 8.For the same population,a sample of n = 16 scores would have a standard error of ____.​
A)​8
B)​6
C)​4
D)​2

Accepted Answer

The answer of For a particular population,a sample of n...

Question 16

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

Accepted Answer

The standard error of the mean (M) is often represented by the symbol σM or σ̄, which is not directly listed among the options. However, option A uses a similar notation with subscript and superscript that could be interpreted as an attempt to represent the standard error of the mean, making it the closest match.

Question 17

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 standard error of the mean (SEM) can be calculated using the formula: SEM = σ/√n, where σ represents the population standard deviation and n represents the sample size. Plugging in the given values, we get:

SEM = 18/√9 = 6

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

Question 18

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 is equal to the mean of the population, which is 80.

The standard error of the distribution of sample means is equal to the standard deviation of the population divided by the square root of the sample size.

Thus,

SE = σ/√n 
SE = 20/√16 
SE = 5

Therefore, the correct answer is B: 80 for the expected value and 5 for the standard error.

Question 19

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

Accepted Answer

The formula for calculating the standard error of the mean (SE) is SE = σ/√n, where σ is the standard deviation of the population and n is the sample size. Here, σ = 36 and n = 4. Substituting these values in the formula, we get SE = 36/√4 = 36/2 = 18. Therefore, the standard error for the distribution of sample means is 18, which corresponds to choice C.

Question 20

Which combination of factors will produce the smallest value for the standard error?​
A)​A large sample and a large standard deviation
B)​A small sample and a large standard deviation
C)​A large sample and a small standard deviation
D)​A small sample and a small standard deviation

Accepted Answer

A large sample size reduces the standard error, while a small standard deviation also reduces the standard error. Therefore, a combination of a large sample size and a small standard deviation will produce the smallest standard error.

Quiz 7: Probability and Samples: the Distribution of Sample Means

What happens to the standard error of M as sample size increases?

The distribution of sample means ____.

What happens to the expected value of M as sample size increases?

What term is used to identify the standard deviation of the distribution of sample means?

What term is used to identify the mean of 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 of M,the mean of the distribution of sample means?

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 random sample of n = 36 scores is selected from a population.Which of the following distributions will definitively be normal?

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 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,then what is the average of all the sample means?

A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively be normal?

Under what circumstances is distribution of sample means normal?

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

If random samples,each with n = 36 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?

For a particular population,a sample of n = 9 scores has a standard error of 8.For the same population,a sample of n = 16 scores would have a standard error of ____.

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

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 .

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

Which combination of factors will produce the smallest value for the standard error?

Quiz 7: Probability and Samples: the Distribution of Sample Means

What happens to the standard error of M as sample size increases?​

The distribution of sample means ____.​

What happens to the expected value of M as sample size increases?​

What term is used to identify the standard deviation of the distribution of sample means?​

What term is used to identify the mean of 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 of M,the mean of the distribution of sample means?​

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 random sample of n = 36 scores is selected from a population.Which of the following distributions will definitively be normal?​

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 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,then what is the average of all the sample means?​

A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively be normal?​

Under what circumstances is distribution of sample means normal?​

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

If random samples,each with n = 36 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?​

For a particular population,a sample of n = 9 scores has a standard error of 8.For the same population,a sample of n = 16 scores would have a standard error of ____.​

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

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 ____.​

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

Which combination of factors will produce the smallest value for the standard error?​