Sampling and Estimation

Question 1

Target population and sampling frame

Answer 1

1. Population being investigated and for what
2. Who is being investigated

Question 2

Central limit theorem

Answer 2

T = X1 + X2 + … + Xn
E(T) = nµ
Var(T) = nσ²
Sd(T) = √n σ

X1 + X2 ≠ 2X , sum of 2 random variables which can have different values, 2X is the outcome of one trial multiplied by 2

Question 3

Distribution of the sample mean x̄

Answer 3

E(x̄) = µ
Var(x̄) = σ²/n

if n>30

Question 4

Types of sampling (5)

Answer 4

1. Small sample from a homogenous population
2. Simple random sampling (whole population available for survey)
3. Systematic sampling (pattern of choice to choose population that is sampled)
4. Cluster sampling (break down a large population into geographical or other groups)
5. Stratified sampling (seperating a population into mutually exclusive sub-groups [weighting] eg. yr 9, yr 10, yr 11)

Question 5

Unbiased estimate
given in formula sheet

Answer 5

1/n-1 Σ(x - x̄)²

further simplification of formula not provided in booklet of mean

Question 6

Confidence interval formulas

Answer 6

x̄ ± z(σ/√n)
p̂ ± z( √(p̂(1 - p̂) / n) )

Question 7

Confidence intervals for proportions

Answer 7

E(p̄) = p
Var(p̄) = pq/n
Sd(p̄) = √pq/n

for binomial np>5 and nq>5