Week 2 - Estimation

Question 1

Population

Answer 1

Is what we want to study, but don’t have immediate access to

Question 2

Sample

Answer 2

A portion of the population

Question 3

Sampling

Answer 3

Method of getting a sample from population

Question 4

Inference

Answer 4

Conclusions from the sample that relate to the population

Question 5

Estimation

Answer 5

Common type of Inference

Use a sample -> Do calculation -> Obtain approximation to do with population

Question 6

Parameter

Answer 6

A property of the population

Question 7

Statistic

Answer 7

A quantity calculated from the sample (data)

Question 8

Estimator (point estimator)

Answer 8

A statistic used for estimating a parameter (Eg: sample mean)

But refers specifically to random variable version (uppercase X)

Question 9

Estimate (point estimate)

Answer 9

The observed value of an estimator

Uses specific data (lowercase x)

Question 10

Sampling variation

Answer 10

Refers to the spread of data points between samples within same population

Question 11

Sampling distribution

Answer 11

A probability distribution of a statistic that comes from choosing random samples of a given population

X¯ ∼ N(µ, σ2/n) - sample mean

Question 12

Random sample

Answer 12

Observations are ‘independent’ and ‘identically distributed’ (iid)

Question 13

Standard error

Answer 13

An estimate of the standard deviation of the estimator

Measures the variability or uncertainty of a sample statistic

se(µ^) = S/√n

Question 14

Confidence interval

Answer 14

Range of values, derived from sample data, that is likely to contain the true population parameter with a certain level of confidence

Pr(L < µ < U) = 0.95
It has a confidence level of 95%
We say that it is a “95% confidence interval for µ”

uˆ ± c * se(µˆ)

Question 15

Central Limit Theorem

Answer 15

States that the sampling distribution of a statistic will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough

Question 16

Interpreting CI

Answer 16

Before any observations:
- X¯ is random
- 95% probability the interval contains µ

After observations:
- x¯ is fixed (not random)
- The realised interval either contains µ or it doesn’t
- There is no longer any probability!

Response answer:
- If we were to repeat the data collection, then 95% of the time the confidence interval we calculate will cover the true value.

Question 17

Paired samples

Answer 17

Involve two related measurements that will improve the certainty of the estimate (Eg: CI)

Pair sampled: Means of the Difference -> mean(x1 - x2)
Unpaired sampled: Difference of the Means -> mean(x1) - mean(x2)