Master Sampling and Sampling Distributions in Statistics for MA Students

Question 1

What is the key difference between probability and non-probability sampling?

Accepted Answer

Probability sampling gives every member of the population an equal chance of being selected, while non-probability sampling does not.

Answer

Non-probability sampling gives every member of the population an equal chance of being selected, while probability sampling does not.

Answer

Probability sampling is always more accurate than non-probability sampling.

Answer

Non-probability sampling is always more accurate than probability sampling.

Question 2

What does the sampling distribution of the mean represent?

Accepted Answer

The distribution of sample means from all possible samples of a given size from a population.

Answer

The distribution of individual data points in a sample.

Answer

The distribution of sample proportions from all possible samples of a given size from a population.

Answer

The distribution of sample standard deviations from all possible samples of a given size from a population.

Question 3

What is the standard error of the mean?

Accepted Answer

The standard deviation of the sampling distribution of the mean.

Answer

The standard deviation of the sample.

Answer

The standard deviation of the population.

Answer

The standard error of the proportion.

Question 4

Which of the following is NOT an advantage of stratified sampling?

Accepted Answer

Low cost and ease of implementation

Answer

Reduced sampling error

Answer

Representation of all strata in the sample

Answer

Ability to estimate population parameters for each stratum

Question 5

What is the primary purpose of using cluster sampling?

Accepted Answer

To reduce costs and time

Answer

To ensure geographic representation

Answer

To improve accuracy

Answer

To reduce bias

Question 6

Which of the following is NOT a type of sampling method?

Accepted Answer

Snowball sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Systematic sampling

Question 7

What is the main source of error in sampling?

Accepted Answer

Sampling error

Answer

Sampling bias

Answer

Measurement error

Answer

Response error

Question 8

Which of the following are potential sources of bias in sampling?

Accepted Answer

All of the above are potential sources of bias in sampling

Answer

Voluntary response bias

Answer

Selection bias

Answer

Non-response bias

Question 9

What is the primary purpose of a sampling distribution?

Accepted Answer

To provide information about the distribution of sample statistics, such as the sample mean or proportion.

Answer

To test hypotheses about the population mean or proportion.

Answer

To select a representative sample from the population.

Answer

To estimate the population mean or proportion.

Question 10

Which of the following is a key characteristic of sampling error?

Accepted Answer

The variation in sample statistics due to random sampling.

Answer

The difference between the sample mean and the population mean.

Answer

The bias introduced by the sampling method.

Answer

The likelihood of selecting an unrepresentative sample.

Question 11

Which sampling method is most likely to produce a representative sample?

Accepted Answer

Simple random sampling

Answer

Systematic sampling

Answer

Convenience sampling

Answer

Quota sampling

Question 12

A sample of 100 students from a population of 1000 students has a sample mean of 75. What is the standard error of the mean?

Accepted Answer

2.5

Answer

5

Answer

7.5

Answer

10

Question 13

Which of the following is the probability of obtaining a sample mean of 68 or less from a population with a mean of 70 and a standard deviation of 5, if the sample size is 50?

Accepted Answer

0.0228

Answer

0.05

Answer

0.1

Answer

0.25

Question 14

What is the main purpose of stratified sampling?

Accepted Answer

To ensure that different subgroups within the population are adequately represented in the sample.

Answer

To reduce sampling error.

Answer

To increase the sample size.

Answer

To make data analysis easier.

Question 15

Which of the following is a potential bias in convenience sampling?

Accepted Answer

The sample is not representative of the target population

Answer

The sample size is too small

Answer

The data is not collected accurately

Answer

The sample is too large

Question 16

What is the key difference between a parameter and a statistic?

Accepted Answer

A parameter is a population characteristic, while a statistic is a sample characteristic.

Answer

A parameter is a statistical measure, while a statistic is a population characteristic.

Answer

A parameter is a numerical value, while a statistic is a categorical value.

Answer

There is no difference between a parameter and a statistic.

Question 17

The sampling error for a sample of size n is inversely proportional to:

Accepted Answer

√n

Answer

n

Answer

n^2

Answer

1/n^2

Question 18

According to the central limit theorem, the distribution of sample means for large samples will be approximately:

Accepted Answer

Normal, regardless of the shape of the population distribution

Answer

The same shape as the population distribution

Answer

Uniform

Answer

Bimodal

Question 19

What is the probability of selecting a sample of size n without replacement from a population of size N?

Accepted Answer

C(N, n)/N

Answer

n/N

Answer

1 - (n/N)

Answer

C(N, n)

Question 20

Which of the following is a measure of the spread of a sampling distribution?

Accepted Answer

Standard error of the mean

Answer

Sampling error

Answer

Margin of error

Answer

Reliability coefficient

Question 21

The process of selecting a sample from a larger population is known as:

Accepted Answer

Sampling

Answer

Experimentation

Answer

Observation

Answer

Analysis

Question 22

What is the primary reason for using sampling in research?

Accepted Answer

To obtain a representative subset of the population

Answer

To reduce the cost of data collection

Answer

To speed up the research process

Answer

To eliminate bias from the data

Question 23

When determining the appropriate sample size for a research study, which of the following factors is NOT a relevant consideration?

Accepted Answer

Researcher's personal preference

Answer

Research question and objectives

Answer

Target population and sampling method

Answer

Desired confidence level and precision

Question 24

When creating a stratified sample, what is the correct sequence of steps?

Accepted Answer

Divide the population into strata, randomly select participants from each stratum, then combine data from all strata

Answer

Randomly select participants from the population, combine data from all strata, then divide the population into strata

Answer

Divide the population into strata, combine data from all strata, then randomly select participants from each stratum

Question 25

In simple random sampling, individuals are randomly selected from a list of subjects. What is the key characteristic of this sampling method?

Accepted Answer

Each individual has an equal chance of being selected.

Answer

The sample is guaranteed to be representative of the entire population.

Answer

The sampling error is always zero.

Question 26

Which sampling method is most likely to produce a representative sample from a population?

Accepted Answer

Random sampling

Answer

Convenience sampling

Answer

Quota sampling

Answer

Cluster sampling

Question 27

What is the term for the difference between the sample mean and the population mean?

Accepted Answer

Sampling error

Answer

Statistical bias

Answer

Standard deviation

Answer

Margin of error

Question 28

What is the probability of obtaining a sample mean that is exactly the same as the population mean?

Accepted Answer

Zero

Answer

25%

Answer

100%

Answer

50%

Question 29

Which statement about the Central Limit Theorem is accurate?

Accepted Answer

It applies to sample means from any population, regardless of its shape.

Answer

It guarantees that sample means will be normally distributed.

Answer

It requires a large population size to be applicable.

Question 30

Which of the following is a primary purpose of using sampling distributions?

Accepted Answer

To make inferences about the population from sample data.

Answer

To reduce the cost and time required for data collection.

Answer

To determine the exact value of the population parameter.

Question 31

What is the probability of obtaining a sample mean that deviates from the population mean by more than two standard deviations?

Accepted Answer

Less than 5%

Answer

More than 25%

Answer

Exactly 10%

Answer

More than 50%

Question 32

Which condition is most likely to violate the assumptions of the Central Limit Theorem?

Accepted Answer

Extreme skewness in the population distribution.

Answer

Sample size is relatively small.

Answer

Population standard deviation is known.

Answer

Data is collected using random sampling.

Question 33

How does increasing the sample size affect the standard deviation of the sampling distribution of the mean?

Accepted Answer

It decreases.

Answer

It becomes non-existent.

Answer

It remains unchanged.

Answer

It increases.

Question 34

Which of the following is NOT a recognized method of sampling?

Accepted Answer

Anecdotal sampling

Answer

Systematic sampling

Answer

Cluster sampling

Answer

Stratified sampling

Question 35

In simple random sampling, the probability of selecting any particular individual from the population is:

Accepted Answer

Equal for all individuals

Answer

Higher for individuals with certain characteristics

Answer

Lower for individuals in smaller groups

Answer

Proportional to the population size

Question 36

The primary purpose of calculating the sampling error is to estimate the:

Accepted Answer

Accuracy of the sample mean

Answer

Outliers in the data

Answer

Statistical significance

Answer

Required sample size

Question 37

According to the Central Limit Theorem, for large enough sample sizes, the sampling distribution of the mean will be approximately:

Accepted Answer

Normal

Answer

Skewed

Answer

Bimodal

Answer

Uniform

Question 38

The primary distinction between a parameter and a statistic is that:

Accepted Answer

A parameter describes the population, while a statistic describes the sample

Answer

A parameter is always larger than a statistic

Answer

A parameter is estimated from a sample, while a statistic is known with certainty

Question 39

Which sampling method has the highest potential for bias?

Accepted Answer

Convenience sampling

Answer

Stratified sampling

Answer

Systematic sampling

Answer

Simple random sampling

Question 40

The relationship between sample size and the standard error of the mean is:

Accepted Answer

As sample size increases, the standard error of the mean decreases

Answer

As sample size increases, the standard error of the mean remains constant

Answer

As sample size increases, the standard error of the mean increases