Question 1

There are more possible samples that can be selected using theoretical sampling than using experimental sampling for any sample size greater than 1.

Accepted Answer

Theoretical sampling allows for greater flexibility and a wider range of possible samples to be selected compared to experimental sampling, which typically follows a strict protocol and may have limited options for sample selection. Therefore, theoretical sampling can offer more potential samples for any given sample size.

Question 2

A sample mean is not always equal to a population mean.

Accepted Answer

This is true because the sample mean is only an estimate of the population mean, and there is always a degree of variability in the sample data that can cause the sample mean to differ from the true population mean.

Question 3

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5.What is the probability of selecting a sample mean equal to at least 12?
A)less than 1%
B)greater than 50%
C)about the same as selecting a sample mean that is at least equal to the population mean
D)equal to the probability of selecting a sample mean that is smaller than 8

Accepted Answer

The answer of A researcher selects a sample of 25...

Question 4

For the experimental sampling strategy,the order in which a participant is selected does not matter,and once selected,each participant is not replaced before sampling again.

Accepted Answer

In non-replacement sampling, the order of selection does not matter and once a participant is selected, they are not replaced before sampling again.

Question 5

Researchers typically sample with replacement,although the development of statistical theory was based on the use of sampling without replacement.

Accepted Answer

Sampling with replacement is not typically used in most research contexts; instead, sampling without replacement is more common because it better reflects the finite nature of most populations under study. Statistical theory, including formulas for variances and standard errors, often accounts for both sampling methods, but practical research, especially involving finite populations, frequently relies on sampling without replacement to ensure all individuals or elements have a chance to be selected without being chosen multiple times.

Question 6

A researcher selects a sample of 9 participants from a population with a mean of 8 and a standard deviation of 3.About 14% of the sample means in this sampling distribution should be between a sample mean of
A)6 and 8
B)5 and 6
C)9 and 10
D)10 and 11

Accepted Answer

We can use the Central Limit Theorem to approximate the sampling distribution of means. According to the theorem, the mean of the sampling distribution will be equal to the population mean and the standard deviation will be equal to the population standard deviation divided by the square root of the sample size.

So,

Mean of sampling distribution = 8 
Standard deviation of sampling distribution = 3 / sqrt(9) = 1

To find the sample means that fall between a certain range, we need to find the corresponding z-scores and use a standard normal distribution table.

For choice A: 
z-score for 6 = (6 - 8) / 1 = -2 
z-score for 8 = (8 - 8) / 1 = 0 
The area between z = -2 and z = 0 is about 0.4772, which is not close to 14%.

For choice B: 
z-score for 5 = (5 - 8) / 1 = -3 
z-score for 6 = (6 - 8) / 1 = -2 
The area between z = -3 and z = -2 is about 0.0668, which is much smaller than 14%.

For choice C: 
z-score for 9 = (9 - 8) / 1 = 1 
z-score for 10 = (10 - 8) / 1 = 2 
The area between z = 1 and z = 2 is about 0.1359, which is close to 14%.

For choice D: 
z-score for 10 = (10 - 8) / 1 = 2 
z-score for 11 = (11 - 8) / 1 = 3 
The area between z = 2 and z = 3 is about 0.1359, which is close to 14%.

Therefore, choices C and D are both possible, but C is the better choice since it is closer to the mean of the sampling distribution.

Question 7

The sampling distribution of the mean has minimum variance.

Accepted Answer

This statement is true. The sampling distribution of the mean has the lowest possible variance when compared to other sampling distributions. This is because the mean of a sample is a more precise estimator of the true population mean than any individual value in the sample. As the sample size increases, the variance of the sampling distribution of the mean decreases, which makes the estimate more accurate.

Question 8

A sampling distribution is a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population.

Accepted Answer

A sampling distribution is a theoretical distribution that shows all possible sample means or sample variances that could be obtained from a population by taking all possible random samples of a specified size from that population.

Question 9

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean that is at least equal to the population mean?
A).50
B)equal to the probability of selecting a sample mean that is at most equal to the population mean
C)both A and B
D)none of the above

Accepted Answer

Since the sample size is greater than 30 (n=49), we can use the central limit theorem which states that the sampling distribution of the sample mean will be approximately 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 (3.5/√49 = 0.5).

Therefore, the probability of selecting a sample mean that is at least equal to the population mean is the same as the probability of selecting a sample mean that is at most equal to the population mean, and both probabilities are equal to 0.5 or 50%. Thus, the answer is C, both A and B.

Question 10

A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM)dollars on groceries each week.Which value is the standard error of the mean?
A)112
B)40
C)100
D)The standard error of the mean is not reported in the article

Accepted Answer

The standard error of the mean is represented by SEM, which in this case is given as 40. Therefore, the correct answer is B.

Question 11

The sampling distribution of the mean is a distribution of all the possible samples of a particular size that can be selected from a given population.

Accepted Answer

This is the definition of the sampling distribution of the mean. It represents the distribution of all possible sample means that could be obtained from a given population.

Question 12

There are 25 possible samples of size 2 that can be selected from a population of 5 people using theoretical sampling.

Accepted Answer

Theoretical sampling is not a method of sampling, but rather a method of data collection in qualitative research. Therefore, it is not applicable in this context of selecting samples from a population. Additionally, if we were using random sampling from a population of 5 people, there would be 10 possible samples of size 2 (i.e. 5 choose 2).

Question 13

An articles states that a sample of 40 participants took 12 ± 2.3 (M ± SEM)seconds to complete a cognitive assessment.Which value is the standard error of the mean?
A)40
B)12
C)2.3
D)The standard error of the mean is not reported in the article

Accepted Answer

The standard error of the mean (SEM) is reported as 2.3 in the article. It represents the estimate of the standard deviation of the population of means obtained from all possible samples of the same size as the one in the study. It is a measure of the variability of the sample means around the true population mean.

Question 14

A sampling distribution is a distribution of scores in a population.

Accepted Answer

A sampling distribution is a distribution of statistics (such as means or proportions) calculated from multiple samples taken from a population, not a distribution of scores in a population.

Question 15

The sample mean is an unbiased estimator,follows the central limit theorem,and has minimum variance.

Accepted Answer

The sample mean is indeed an unbiased estimator, follows the central limit theorem and has minimum variance.

Question 16

How is the standard error of the mean typically reported in a graph?
A)using error bars
B)by plotting sample means
C)by listing group names along the x-axis
D)it is never reported in a graph

Accepted Answer

The standard error of the mean is typically reported in a graph using error bars. These bars indicate the range of values within which we can reasonably assume the true population mean lies with a certain level of confidence.

Question 17

The central limit theorem states that the sample mean will equal the population mean on average.

Accepted Answer

The answer of The central limit theorem states that the...

Question 18

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20.About 68% of the sample means in this sampling distribution should be between a sample mean of
A)34 and 40
B)34 and 38
C)38 and 44
D)36 and 40

Accepted Answer

The answer of A researcher selects a sample of 100...

Question 19

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5.What is the probability of selecting a sample mean that is at least two standard deviations larger than the population mean?
A).0228
B).4772
C).9772
D)equal to the probability of selecting a sample mean that is at least two standard deviations below the mean

Accepted Answer

The probability of selecting a sample mean that is at least two standard deviations larger than the population mean is found using the standard normal distribution (Z-distribution). The Z-score for two standard deviations above the mean is 2. The Central Limit Theorem allows us to treat the distribution of sample means as normally distributed if the sample size is sufficiently large (n ≥ 30 is a common rule of thumb, but n = 25 is often considered large enough for the approximation to be useful). The standard error of the mean (SEM) is the standard deviation of the population divided by the square root of the sample size. In this case, the SEM = 5 / sqrt(25) = 1. The Z-score for a sample mean that is two standard deviations (10 units in this context, since the population standard deviation is 5 and we're considering 2 of these) above the population mean of 10 is (20 - 10) / 1 = 10. However, since we're looking for the probability of being at least two standard deviations above, we're interested in the tail beyond Z = 2. Looking up the Z-score of 2 in standard normal distribution tables or using a calculator gives us the area to the left of Z = 2, which we subtract from 1 to find the tail probability. This gives us approximately 0.0228, indicating a small probability of selecting such a sample mean by chance.

Question 20

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean of 13 or larger from this population?
A)equal to the probability of selecting a score above the mean
B)about one standard deviation below the mean
C)less than .03
D)greater than .31

Accepted Answer

To solve this problem, we need to use the formula for the standard error of the mean: standard deviation / square root of sample size. In this case, the standard error of the mean is 3.5 / sqrt(49) = 0.5. Then, we can use the z-score formula to find the probability of selecting a sample mean of 13 or larger: z = (13 - 12) / 0.5 = 2. The probability of a z-score of 2 or greater is less than 0.03, which means the answer is (C) less than 0.03.

Quiz 7: Hypothesis Testing: Significance, Effect Size, and Power

There are more possible samples that can be selected using theoretical sampling than using experimental sampling for any sample size greater than 1.

A sample mean is not always equal to a population mean.

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5.What is the probability of selecting a sample mean equal to at least 12?

For the experimental sampling strategy,the order in which a participant is selected does not matter,and once selected,each participant is not replaced before sampling again.

Researchers typically sample with replacement,although the development of statistical theory was based on the use of sampling without replacement.

A researcher selects a sample of 9 participants from a population with a mean of 8 and a standard deviation of 3.About 14% of the sample means in this sampling distribution should be between a sample mean of

The sampling distribution of the mean has minimum variance.

A sampling distribution is a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population.

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean that is at least equal to the population mean?

A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM) dollars on groceries each week.Which value is the standard error of the mean?

The sampling distribution of the mean is a distribution of all the possible samples of a particular size that can be selected from a given population.

There are 25 possible samples of size 2 that can be selected from a population of 5 people using theoretical sampling.

An articles states that a sample of 40 participants took 12 ± 2.3 (M ± SEM) seconds to complete a cognitive assessment.Which value is the standard error of the mean?

A sampling distribution is a distribution of scores in a population.

The sample mean is an unbiased estimator,follows the central limit theorem,and has minimum variance.

How is the standard error of the mean typically reported in a graph?

The central limit theorem states that the sample mean will equal the population mean on average.

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20.About 68% of the sample means in this sampling distribution should be between a sample mean of

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5.What is the probability of selecting a sample mean that is at least two standard deviations larger than the population mean?

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean of 13 or larger from this population?