1.5: sampling methods

Question 1

Sampling

Answer 1

used to get information about a parameter of a population

–>A statistic from a sample is used because measuring the parameter from the population is either not possible or cost-prohibitive

Question 2

The two types of sampling methods

Answer 2

Probability sampling

Non-probability sampling

Question 3

Probability sampling

Answer 3

Every member of the population has the same chance of being selected

The sample created is usually representative of the population.

Question 4

Non-probability sampling

Answer 4

Non-probability considerations (such as the convenience to access data or the sampler’s judgment) are used in sample selection

The sample created may not be representative of the population

Question 5

sampling methods resulting from probability sampling

Answer 5

Simple Random Sampling

Systematic Sampling

Stratified Random Sampling

Cluster Sampling

Question 6

sampling methods resulting from non-probability sampling

Answer 6

Convenience Sampling

judgmental Sampling

Question 7

simple random sampling

Answer 7

each population element has an equal probability of being selected

also often called just a random sample

requires randomness

–> could be done by assigning each member of the population a random number and using a computer program or table of random digits to choose the members

Question 8

when is simple random sampling useful

Answer 8

when the data is homogenous

Question 9

systematic sampling

Answer 9

chooses every kth member until the desired sample size is reached

useful if the analyst cannot identify all members of a population

Question 10

The sampling error

Answer 10

the difference between the sample statistic and the population parameter (e.g., the sample mean and the population mean)

Question 11

The sampling distribution of a statistic

Answer 11

the distribution of all statistic values calculated from the same sample size from the same population

Question 12

stratified random sampling

Answer 12

the population is first divided into subgroups (strata) based on some criteria

Simple random samples are drawn from each subgroup in proportion to the subgroup’s relative size to the entire population

This method results in less variance than estimates derived from simple random sampling

It makes sure that the population subdivisions of interest are captured in the sample set

Question 13

what is stratified random sampling used for?

Answer 13

commonly used to create portfolios that are meant to track a bond index

–> First, the entire population of bonds in the index is divided into subgroups based on factors such as maturity, sector, credit quality, etc.

–> The manager then selects a sampling of bonds from within each subgroup

Question 14

cluster sampling

Answer 14

divides the population into subgroups known as clusters

Question 15

difference between stratified random sampling and cluster sampling

Answer 15

unlike stratified random sampling which defines subgroups based on certain criteria, cluster sampling divides the entire sample into mini-representations of the population

–> In other words, each cluster will consist of samples with different characteristics

Question 16

cluster sampling steps

Answer 16

1. Certain clusters are selected using simple random sampling.
2. a one-stage cluster sampling selects all the members in the sampled clusters, while a two-stage cluster sampling randomly selects a subsample from each sampled cluster.

Question 17

The major advantage of cluster sampling and its con

Answer 17

it is a time-efficient, cost-effective method of probability sampling a large population

con: the accuracy of the results can be skewed if the chosen clusters are not representative of the overall population

Question 18

Convenience sampling

Answer 18

selects samples based on how accessible they are for the researcher

This method allows samples to be collected quickly at a low cost

However, since data are selected conveniently, they may not be representative of the population

Question 19

judgmental sampling,

Answer 19

the researcher handpicks samples based on their knowledge and professional judgment

This sampling method is beneficial when there is a time constraint because the researcher can quickly select a more representative sample using their expertise

However, the samples selected may be subject to the researcher’s bias, resulting in skewed results

Question 20

Which of the following methods is most appropriate to use when only some members of a finite population can be identified?

A
Systematic sampling

B
Simple random sampling

C
Stratified random sampling

Answer 20

A
Systematic sampling

Question 21

Perkiomen Kinzua, a seasoned auditor, is auditing last year’s transactions for Conemaugh Corporation. Unfortunately, Conemaugh had a very large number of transactions last year, and Kinzua is under a time constraint to finish the audit. He decides to audit only the small subset of the transaction population that is of interest and to use sampling to create that subset.

The most appropriate sampling method for Kinzua to use is:

A
judgmental sampling.

B
systematic sampling.

C
convenience sampling.

Answer 21

A
judgmental sampling.

Question 22

The central limit theorem states the following:

Answer 22

The sampling distribution of a sample mean X¯ will be approximately normal with a mean of μ (the population mean) and variance of (σ^2)/n, provided the sample size n is large (usually greater than 30)

This is true for a population with any probability distribution provided it has a finite variance σ^2
.

Question 23

According to the central limit theorem, when the sample size increases, what will happen to the distribution of the sample mean?

Answer 23

it will converge to a normal distribution

This is true regardless of the actual distribution of the population

Notice that the variance of the sample mean is (σ^2)/n.

Assuming a constant population variance σ, when n increases, the variance of the sample mean decreases.

–> Said differently, with a large enough sample, the sample mean X¯ will be very close to the population mean μ

Question 24

How is the standard error of the sample mean X¯ defined as?

Answer 24

σX¯ = σ/√n or sX¯ = s/√n

–> The first is used if the population standard deviation σ is known, which is rare

–> The second definition requires an estimate of s

Question 25

how do we calculate the s in a standard error if we need to estimate it?

Answer 25

s^2 = ∑(Xi − X¯)^2 / (n−1)

Question 26

the difference between the standard error and standard deviation

Answer 26

the standard error describes the accuracy of an estimate (from sampled data) relative to its true value

the standard deviation describes the dispersion of data around its mean

Question 27

A population has a non-normal distribution with mean μ and variance σ^2

The sampling distribution of the sample mean computed from samples of large size from that population will most likely have:

A
the same distribution as the population distribution.

B
its mean approximately equal to the population mean.

C
its variance approximately equal to the population variance.

Answer 27

B
its mean approximately equal to the population mean.