Statistics

Question 1

Assumptions for binomial model to be valid

Answer 1

1. Probability remains constant
2. Events occur independently of one another
3. There are only two possibilities for each outcome

Question 2

Describe how to collect a random sample of k out of N items

Answer 2

1. Give each item a number from 1, 2, … , N
2. Generate a random number between 1 and N using a calculator
3. Continue until k different items have been selected

Question 3

3 disadvantages of census

Answer 3

1. Takes a lot of time, effort and money to carry out
2. Can be difficult to make sure all members are surveyed
3. Impractical if tested items are used up or damaged

Question 4

Advantage of census

Answer 4

Gives an unbiased, accurate representation of the whole population

Question 5

Advantage of simple random sampling

Answer 5

Completely unbiased - each member has an equal chance of being selected

Question 6

Advantage/disadvantage of systematic sample

Answer 6

• Should give an unbiased sample
• But if interval coincides with a pattern, the sample could be biased

Question 7

Number needed for each category in stratified sampling

Answer 7

(size of category in pop. ÷ total pop. size) x (total sample size)

Question 8

2 advantages of stratified sampling

Answer 8

• If categories are disjoint, should give a representative sample
• Useful when results vary depending on categories

Question 9

Disadvantage of stratified sampling

Answer 9

The extra detail needed can make it more time consuming and expensive

Question 10

Describe method for quota sampling

Answer 10

1. Divide population into categories
2. Give each category a quota (the number of members to sample)
3. Collect data until quotas are met in all categories (without random sampling)

Question 11

2 advantages of quota sampling

Answer 11

1. Easy for interviewer as they don’t need a list of the whole population
2. Non-response is less of a problem

Question 12

Disadvantage of quota

Answer 12

Can be biased by the interviewer as selection isn’t random

Question 13

Advantage of opportunity sampling

Answer 13

Data can be gathered quickly and easily

Question 14

Disadvantage of opportunity sampling

Answer 14

It isn’t random and can be very biased - no attempt to make the sample representative

Question 15

Describe method for cluster sampling

Answer 15

1. Divide the population into clusters covering the whole population
2. Randomly select clusters to use in the sample, based on the required sample size
3. Either use all members of the selected clusters (one-stage cluster sample) or randomly sample within each sample (two-stage cluster sample)

Question 16

2 drawbacks of cluster sampling

Answer 16

• Results can be less representative
• Not always possible to separate the population into cluster in a natural way

Question 17

Describe method for sampling using self-selection/volunteer sampling

Answer 17

1. Advertise or appeal to the whole population
2. Either use everyone who responds as the sample, or take a sample of them that best represents the population

Question 18

3 advantages of self-selection/volunteer sampling

Answer 18

1. Requires little time or effort in finding sample members
2. Non-response is less of an issue
3. Sometimes is the only way to find member of a population

Question 19

Disadvantage of self-selection/volunteer sampling

Answer 19

There can easily be trends within the respondents, such as people having strong opinions, which would lead to bias