MODULE 7.1 SAMPLING TECHNIQUES AND THE CENTRAL LIMIT THEOREM

Question 1

Q: What is probability sampling?

Answer 1

A: Sampling where the probability of each sample member being selected is known.

Question 2

Q: Define simple random sampling.

Answer 2

A: A method where each item in the population has an equal probability of being selected.

Question 3

Q: What is systematic sampling?

Answer 3

A: Selecting every nth member from a population.

Question 4

Q: Explain stratified random sampling.

Answer 4

A: Dividing the population into subgroups (strata) and taking random samples from each, based on their size relative to the population.

Question 5

Q: What is the main advantage of stratified sampling?

Answer 5

A: Ensures representation from all subgroups in the population.

Question 6

Q: Define cluster sampling.

Answer 6

A: Sampling based on subsets (clusters) assumed to represent the entire population.

Question 7

Q: Contrast one-stage and two-stage cluster sampling.

Answer 7

A: One-stage includes all data in selected clusters; two-stage selects random samples within each chosen cluster.

Question 8

Q: What is convenience sampling?

Answer 8

A: Selecting sample data based on ease of access, often leading to higher sampling error.

Question 9

Q: Define judgmental sampling.

Answer 9

A: Using researcher judgment to select specific data items, which may introduce bias.

Question 10

Q: What is the central limit theorem?

Answer 10

A: It states that the sampling distribution of the sample mean approaches a normal distribution as sample size (n) becomes large, typically n ≥ 30. the population mean of u and variance of sd2 / n (or variance / n)

Question 11

Q: List the properties of the central limit theorem.

Answer 11

Sampling distribution of sample means is approximately normal for n ≥ 30.

Mean of the population (μ) equals the mean of the sampling distribution.

Variance of sample means is population variance divided by sample size.

Question 12

Q: What is the standard error of the sample mean formula when population standard deviation (σ) is known?

Answer 12

SE = SD / SQRT(n)

Question 13

Q: How is the standard error calculated when population standard deviation is unknown?

Answer 13

using the sample standard deviation. use S/SQRT(n)

Question 14

Q: How does sample size affect the standard error?

Answer 14

A: Increasing sample size decreases the standard error, making sample means closer to the true population mean.

Question 15

Q: What is the jackknife method?

Answer 15

A: A resampling method where each sample mean is calculated with one observation removed.

Question 16

Q: Define the bootstrap method.

Answer 16

A: A resampling method where repeated samples of size n are drawn from the dataset, with replacement, to estimate the sampling distribution.

Question 17

Q: Which resampling method is more computationally demanding: jackknife or bootstrap?

Answer 17

Bootstrap

Question 18

Q: What is the key difference between stratified sampling and cluster sampling?

Answer 18

A: Stratified sampling ensures representation from all subgroups, while cluster sampling assumes clusters represent the population.

Question 19

Q: To apply the central limit theorem, what is the usual minimum sample size?

Answer 19

30

Question 20

Q: In the central limit theorem, what happens to the variance of the sample mean as sample size increases?

Answer 20

A: It decreases, leading to a smaller standard error.

Question 21

how do we calculate for SE when we don’t know the population SD????

Answer 21

just use sample SD. We usually won’t know the population SD so keep an eye.

it would still be SD / sqrt(n)

Question 22

what happens to SE when N becomes bigger?

Answer 22

SE goes down

Question 23

When do you use SE vs SD??

Answer 23

SE is telling you about X (sample) that we use to estimate the u. Tells us about the dispersion of the sample mean around the distributions true population mean

SD is telling us about the dispersion of a SINGLE observation from a distribution

Question 24

Student’s t distribution

Answer 24

The sample mean follows the student’s t distribution instead of a normal distribution with degrees of freedom of n-1

Question 25

What is the student’s t tabl e

Question 26

draw a diagram of when to use and not to use z vs t values for SE

Question 27

When do you walk away from the data

Answer 27

When you have a nonnormal distribution and a small data size walk away