Sampling Distributions

Question 1

Sampling distribution

Answer 1

A sampling distribution is a distribution of all of the possible values of a statistic for a given size sample selected from a population.

Sampling Distribution of the Mean

Sampling Distribution of the Proportion

Question 2

Standard error of the mean

Answer 2

Different samples of the same size from the same population will yield different sample means.
A measure of the variability in the mean from sample to sample is given by the Standard Error of the Mean. Note that the standard error of the mean decreases as the sample size increases.
(This assumes that sampling is done with replacement, or that sampling is done without replacement, from a large or infinite population).

Question 3

If the population is not normal

Answer 3

We can apply the Central Limit Theorem, which states that regardless of the shape of individual values in the population distribution, as long as the sample size is large enough (generally n ≥ 30) the sampling distribution of XBAR will be approximately normally distributed with:

Question 4

Characteristics pf the sampling distribution of the proportion

Answer 4

π is the proportion of items in the population with a characteristic of interest.
p is the sample proportion and provides an estimate of π

Question 5

Sampling Distribution of the Proportion

Answer 5

Selecting all possible samples of a certain size, the distribution of all possible sample proportions is the sampling distribution of the proportion.

Question 6

Standard Error of the Proportion

Answer 6

The underlying distribution of the sample proportion is binomial.

It can be approximated by normal distribution if ≥ 5 and ≥ 5 with the resulting mean equal to and standard error equal to:

Question 7

Reasons for taking a sample

Answer 7

Less time-consuming than a census.
Less costly to administer than a census.
Less cumbersome and more practical to 
	administer than a census of the targeted 
	population.

Question 8

2 types of samples used

Answer 8

Non-probability sample:
Items included are chosen without regard to their probability of occurrence.

Probability sample:
Items in the sample are chosen on the basis of known probabilities.

Question 9

Simple random sampling

Answer 9

Every individual or item from the frame (N) has an equal chance of being selected (1/N).

Selection may be with replacement or without replacement.

Samples can be obtained from a table of random numbers or computer random number generators.

Simple to use but may not be a good representation of the population’s underlying characteristics.

Question 10

Systematic sampling

Answer 10

Divide frame of N individuals into n groups of k individuals: k = N/n.

Randomly select one individual from the 1st group.

Select every kth individual thereafter.

Like simple random sampling, simple to use but may not be a good representation of the population’s underlying characteristics.

Question 11

Stratified sampling

Answer 11

Divide population into two or more subgroups (called strata) according to some common characteristic.

A simple random sample is selected from each subgroup, with sample sizes proportional to strata sizes – called proportionate stratified sampling.

Samples from subgroups are combined into one.

Question 12

Stratified sampling pros

Answer 12

More efficient than simple random sampling or systematic sampling because of assured representation of items across entire population.
Homogeneity of items within each stratum provides greater precision in the estimates of underlying population parameters.

Question 13

Cluster samples

Answer 13

Population is divided into several ‘clusters’, each representative of the population e.g. postcode areas, electorates etc.

A simple random sample of clusters is selected:
All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique.

Question 14

Cluster sampling pros

Answer 14

More cost effective than random sampling, especially if population is geographically widespread.
Often requires a larger sample size compared to simple random sampling or stratified sampling for same level of precision.

Question 15

Evaluating survey worthiness

Answer 15

What is the purpose of the survey?

Is the survey based on a probability or non-probability sample?

Question 16

Survey errors

Answer 16

Coverage error – appropriate or adequate frame?
Non-response error – results in non-response bias.
Measurement error – ambiguous wording, halo effect or respondent error.
Sampling error – always exists and is the difference between sample statistic and population parameter.

Question 17

1

Answer 17

Step 1 normdist

Question 18

2

Answer 18

Step 3 normdist

Question 19

3

Answer 19

Data for sampling distribution data

Question 20

4

Answer 20

Summary measures for the pop dist

Question 21

5

Answer 21

Sampling distribution graph

Question 22

6

Answer 22

Sample means

Question 23

7

Answer 23

Summary measures of sampling dist

Question 24

8

Answer 24

Comparing pop with sampling dist

Question 25

9

Answer 25

Standard error of the mean

Question 26

10

Answer 26

If the pop is normal

Question 27

11-12

Answer 27

Sampling dist properties

Question 28

13-15

Answer 28

Central limit theorem

Question 29

16

Answer 29

z formula for sampling distribution

Question 30

17

Answer 30

Sampling dist example data

Question 31

18-19

Answer 31

Central limit theorem example

Question 32

20-21

Answer 32

Sampling distribution of the proportion

Question 33

22

Answer 33

Standard error of the proportion

Question 34

23

Answer 34

z formula for proportions

Question 35

24-26

Answer 35

Sampling diet of the proportion example

Question 36

27

Answer 36

Types of samples used

Question 37

28

Answer 37

Probability samples

Question 38

29

Answer 38

Systematic sampling example

Question 39

30

Answer 39

stratified sampling

Question 40

31

Answer 40

cluster sampling