Random & non-random Sampling

Question 1

what are the advantages of pilot surveys?

Answer 1

a) test appropriateness
b) ensures instructions are able to be followed
c) saves on resources

Question 2

What are the types of non-random sampling?

Answer 2

a) quota
b) self-selected
c) convenience

Question 3

what are the disadvantages of quota sampling?

Answer 3

a) important groups may be overlooked when determining quotas
b) biased

Question 4

what are the disadvantages of self-selected sampling?

Answer 4

a) tends to result in more extreme/biased results as volunteers are more motivated to take part
b) differ from rest of pop

Question 5

what are the disadvantages of convenience sampling?

Answer 5

a) biased due to under-coverage

Question 6

Why is random sampling essential?

Answer 6

a) representative
b) valid results
c) non-biased

Question 7

How do you calculate the population variance?

Answer 7

a) (sum of the values - mean) squared / n

Question 8

What is sample variance?

Answer 8

(n / (n-1)) x sigma sqrd

Question 9

How do we define if a parameter is unbiased?

Answer 9

a) if E(parameter estimator) = parameter
b) so bias is: B(parameter estimator) = E(parameter estimator) - parameter
c) unbiased if B = 0

Question 10

How do you determine precision of an estimator?

Answer 10

a) smaller the variance, the more precise and unbiased

Question 11

What must be considered when determining sampling distribution of estimators?

Answer 11

a) only appropriate for random sampling methods where probability of selecting any sample is known
b) otherwise, statistical inference should not be carried out

Question 12

What is the aim of sampling theory?

Answer 12

to produce sampling schemes which give the minimum variance unbiased estimators

Question 13

describe the process of simple uniform random sampling

Answer 13

a) sample population randomly without replacement
b) at any stage, all remaining units are equally likely to be chosen

Question 14

how to calculate sample variance (s squared)

Answer 14

> unbiased estimate of population variance

Question 15

what is the estimated standard error of SRS?

Answer 15

a) sqrt of the variance

Question 16

Why sample without replacement?

Answer 16

a) doesn’t allow replication
b) including units more than once reduces information

Question 17

What effect does sampling with replacement have?

Answer 17

a) results in independent observations being obtained
b) probability of selecting a particular observation is unaffected by the selection of previous observations.

Question 18

What is the finite population correction?

Answer 18

a) used under sampling with replacement
b) shows the difference between the forms of variances
c) calculated by 1 - f

Question 19

is sampling with or without replacement preferred?

Answer 19

a) variance of SRS without replacement is lower
b) so without replacement is more precise

Question 20

What happens to the properties of sampling with and without replacement if the sample size is small in relation to the population?

Answer 20

a) fpc becomes closer to 1
b) they have essentially the same properties

Question 21

What to do if population size is known when assessing forms of variance?

Answer 21

use the fpc in calculations

Question 22

how do you calculate confidence interval for population mean?

Answer 22

mean +/- 1.96 x sd

Question 23

When does central limit theorem kick in?

Answer 23

when n > 30

Question 24

How do you calculate the error bound for a parameter?

Answer 24

a) 1.96 x estimated standard error of parameter
b) In about 95% of samples the estimate θ ̂ will be within that distance of the actual value of θ

Question 25

Which statistics do you use when the population is normal and variance is known? (SRS)

Answer 25

a) x bar exactly follows normal distribution with mean mu and variance:

Question 26

Which statistics do you use when the population is normal and variance is unknown? (SRS)

Answer 26

a) t distribution b) gives a wider more conservative interval

Question 27

Which statistics do you use when the population is not normal and n > 30? (SRS)

Answer 27

A) X bar approximately follows a normal distribution with mean mu and variance:

Question 28

Which statistics do you use when the population is not normal and n < 30? (SRS)

Answer 28

non-parametric methods

Question 29

What is B in sample size calculations? (SRS)

Answer 29

a) the error bound b) 1.96 x s.e (estimator)

Question 30

What is the estimated standard error of an estimated population total?

Answer 30

Question 31

How do you estimate a 95% confidence interval for proportion p?

Answer 31

a) where final term represents estimated standard error of estimator

Question 32

When estimating a total, what can be used in place of the sample mean?

Answer 32

a) proportion of population with characteristic of interest b) sub in place of x bar

Question 33

What do you do if estimating sample size based on proportion but p is unknown?

Answer 33

a) use p from pilot survey/study b) for conservative sample size estimate, use p = 0.5