Stats chapter 1 (populations, samples and random sampling)

Question 1

What is a population?

Answer 1

The whole set of items that are of interest
(e.g. all of the lightbulbs in a factory)

Question 2

What is a sample?

Answer 2

Some subset of the population intended to represent the population

Question 3

What is a sampling unit?

Answer 3

Each individual thing in the population that can be sampled

Question 4

What is a sampling frame?

Answer 4

when sampling units of a population are individually named or numbered to form a list

Question 5

What are the two things data could be collected from?

Answer 5

From a sample or from the entire population (census)

Question 6

What is a census?

Answer 6

Data collected from the entire population

Question 7

What are the advantages of a census? (1)

Answer 7

• should give completely accurate results

Question 8

What are the disadvantages of a census? (3)

Answer 8

• time consuming and expensive
• larger volume of data to process
• can’t be used when the testing involves destruction (e.g. finding out the number of biscuits in a machine filled box/bag)

Question 9

What are the advantages of a sample? (3)

Answer 9

• cheaper
• quicker
• less data to process

Question 10

What are the disadvantages of a sample? (2)

Answer 10

• data may not be accurate
• data may not be large enough to represent small sub-groups

Question 11

What is Random sampling?

Answer 11

where we want each sampling unit in our sampling frame to have an equal chance of being chosen, in order to avoid bias

Question 12

What are the three ways of doing Random sampling?

Answer 12

1. Simple random sampling
2. Systematic sampling
3. Stratified sampling

Question 13

What is simple random sampling?

Answer 13

where every sampling unit in the sampling frame has an equal chance of being selected

Question 14

How do you carry out simple random sampling?

Answer 14

In a sampling frame, each item has an identifying number. Use a random number generator or ‘lottery sampling’ (names in a hat) to chose numbers

Question 15

What are the advantages of simple random sampling? (3)

Answer 15

• bias free
• easy and cheap to implement
• each number has a known equal chance of being selected

Question 16

What are the disadvantages of simple random sampling? (2)

Answer 16

• not suitable when the population size is large
• sampling frame is needed

Question 17

What is systematic sampling?

Answer 17

required elements are chosen at regular intervals in an ordered list

Question 18

How do you carry out systematic sampling?

Answer 18

Take every kth element, where k = pop size (N) / sample size (n), starting at a random number between 1 and k

Question 19

What are the advantages of systematic sampling? (2)

Answer 19

• simple and quick to use
• suitable for large samples/populations

Question 20

What are the disadvantages of systematic sampling? (2)

Answer 20

• sampling frame again needed
• can introduce bias if sampling frame is not random

Question 21

What is stratified sampling?

Answer 21

Population divided into groups (strata) and a simple random sample is carried out in each group

Question 22

What is a strata?

Answer 22

A distinct group

Question 23

When is stratified sampling used?

Answer 23

when the sample is large and the population naturally divides into groups

Question 24

How do you carry out stratified sampling?

Answer 24

Use the same proportion (sample size /pop size) sampled from each strata

Question 25

What are the advantages of stratified sampling? (2)

Answer 25

• reflects population structure
• guarantees proportional representation of groups within population

Question 26

What are the disadvantages of stratified sampling? (2)

Answer 26

• population must be clearly classified into distinct strata
• selection within each stratum suffers from the same disadvantages as simple random sampling