Sampling Methods and Classifications5 min
Sampling methods are the rules used to select a subset of a population. They are broadly classified into probability sampling and non-probability sampling. Probability sampling ensures every member of the population has an equal chance of being selected, leading to representative samples with higher accuracy and reliability. This category includes Simple Random Sampling (homogenous data), Systematic Sampling (selecting every kth member), Stratified Random Sampling, and Cluster Sampling. Non-probability sampling depends on factors like researcher judgment or convenience, carrying a significant risk of generating non-representative samples. Examples include Convenience Sampling (based on accessibility) and Judgmental Sampling (based on professional judgment).

Key Points

  • Probability sampling provides equal selection chances and higher reliability.
  • Systematic sampling involves selecting every kth member.
  • Non-probability sampling includes Convenience and Judgmental sampling.
  • Sampling error is the difference between the observed sample statistic and the population parameter.
Stratified vs. Cluster Sampling6 min
Stratified Random Sampling involves dividing the population into subpopulations (strata) and drawing samples from each proportional to their size. This method guarantees representation of specific subdivisions (e.g., bond indexing) and produces estimates with greater precision (lower variance). In contrast, Cluster Sampling divides the population into groups (clusters) and selects entire clusters (one-stage) or subsamples within them (two-stage). While Cluster Sampling is cost and time-efficient, especially for geographic parameters, it usually yields lower accuracy compared to stratified sampling because a single cluster may not represent the entire population.

Key Points

  • Stratified sampling increases precision and guarantees representation.
  • Bond indexing is a common application of stratified sampling.
  • Cluster sampling is cost-effective but generally less accurate.
  • One-stage cluster sampling includes all members of the selected clusters.
Central Limit Theorem and Standard Error5 min
The Central Limit Theorem (CLT) asserts that for a sample size (n) of 30 or more, the sampling distribution of the sample mean will approach a normal distribution, regardless of the population's underlying distribution. The mean of this sampling distribution equals the population mean, and its standard deviation is known as the Standard Error (SE). The SE is calculated as the population standard deviation divided by the square root of n. If the population standard deviation is unknown, the sample standard deviation is used as an estimate. The SE measures how precise the estimate of the population parameter is.

Key Points

  • CLT applies when sample size n is greater than or equal to 30.
  • Sampling distribution approaches a normal distribution.
  • Standard Error = Population SD / square root of n.
  • Standard Error measures the precision of the sample mean estimate.
Resampling Techniques: Bootstrap and Jackknife4 min
Resampling methods are used when analytical formulas are difficult to apply or when estimating the sampling distribution directly from the data. Bootstrapping involves repeatedly drawing samples of the same size as the original from the original dataset with replacement. It is often called model-free or non-parametric resampling. The Jackknife method selects samples by taking the original observed data and leaving out one observation at a time (without replacement). Unlike bootstrapping, which can yield different results due to random sampling, the Jackknife method produces the same result for every run because its procedure is deterministic.

Key Points

  • Bootstrapping draws samples with replacement.
  • Jackknife leaves out one observation at a time (n samples for size n).
  • Jackknife produces deterministic results; Bootstrap produces random results.
  • Both methods rely on repetitive sampling to estimate parameters.

Questions

Question 1

Which of the following best describes a key characteristic of probability sampling?

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Question 2

Which sampling method involves dividing the population into subpopulations and drawing samples from each proportional to their relative size?

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Question 3

If a researcher selects every 50th member of a population list to create a sample, which method is being used?

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Question 4

What is the primary advantage of stratified random sampling over simple random sampling?

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Question 5

In the context of sampling, what is 'sampling error'?

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Question 6

Which sampling technique is most commonly used for bond indexing?

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Question 7

Cluster sampling is considered most advantageous in terms of:

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Question 8

What distinguishes 'two-stage' cluster sampling from 'one-stage' cluster sampling?

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Question 9

Which of the following is a risk associated with non-probability sampling?

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Question 10

Auditors using their professional knowledge to select specific transactions for review is an example of:

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Question 11

Which sampling method is most appropriate when the population data is homogeneous?

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Question 12

According to the Central Limit Theorem (CLT), the sampling distribution of the mean will be approximately normal if the sample size is:

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Question 13

Under the Central Limit Theorem, the mean of the sampling distribution is equal to:

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Question 14

If a population has a standard deviation of 20 and a sample size of 100 is drawn, what is the standard error of the sample mean?

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Question 15

Standard error is best defined as:

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Question 16

When the population standard deviation is unknown, the standard error is estimated using:

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Question 17

Bootstrapping is a resampling method that involves:

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Question 18

A key difference between Bootstrapping and Jackknife resampling is that:

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Question 19

How many repetitions are usually required for the Jackknife method on a sample of size n?

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Question 20

In Bootstrapping, the size of each re-sample is:

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Question 21

Which method is also referred to as 'model-free re-sampling' or 'non-parametric re-sampling'?

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Question 22

If a sample mean is 50, the population standard deviation is 10, and the sample size is 25, what is the standard error?

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Question 23

Which sampling method is prone to 'skewed results' due to the bias of the researcher?

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Question 24

What is a characteristic of Convenience Sampling?

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Question 25

Which method is useful when population members cannot be coded or identified?

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Question 26

In Stratified Random Sampling, samples from each stratum are drawn:

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Question 27

Which of the following statements regarding Cluster Sampling is correct?

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Question 28

A distribution of all distinct possible values that a statistic can assume when computed from samples of the same size is called:

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Question 29

The Central Limit Theorem implies that as the sample size increases, the standard error of the sample mean:

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Question 30

If standard error is calculated as s/sqrt(n), what does 's' represent?

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Question 31

Which resampling method replaces each item drawn for the next draw?

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Question 32

If you are conducting a survey and choose to interview people simply because they are easily accessible at a shopping mall, you are using:

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Question 33

In the Jackknife method, if the original sample has 10 observations, how many re-samples are created?

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Question 34

Which of the following is true regarding the sample mean in relation to the Central Limit Theorem?

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Question 35

Sample standard deviation (Sx) approaches what value according to the Central Limit Theorem?

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Question 36

If we want to find out how precise the estimate of a population parameter from sampled data is, which statistic should be used?

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Question 37

In stratified random sampling, all strata are included, but in cluster sampling:

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Question 38

Which sampling method guarantees that population subdivisions of interest are represented?

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Question 39

Which of the following is a type of non-probability sampling?

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Question 40

For a sample size of 64 and a population standard deviation of 16, calculate the standard error.

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Question 41

What is the result of using a systematic sampling plan?

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Question 42

Which method involves selecting a sample by handpicking elements based on knowledge?

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Question 43

The standard error formula s/sqrt(n) is used when:

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Question 44

Which of the following describes 'One-stage cluster sampling'?

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Question 45

Probability sampling is generally preferred over non-probability sampling because:

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Question 46

If a sample size n=49 and sample standard deviation s=14, what is the estimated standard error?

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Question 47

In the context of Big Data, bootstrapping is often called:

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Question 48

What is the relationship between the standard deviation of the sampling distribution and the standard error?

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Question 49

Which sampling method is noted for having 'level of sampling accuracy could be limited'?

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Question 50

If a sample has 100 observations, determining the appropriate number of repetitions for Bootstrapping is:

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