Statistical Inference (cont)

What is standard error of a sample statistic?

The standard deviation of its sampling distribution.

How do you find the standard error (mean)?

σ vX ̅ = σ/√n

How do you find the standard error in terms of proportion of a population?

σ vp ̂ =√p(1-p) / n

What are the two ways you can estimate population parameters?

• Point Estimation

• Interval Estimation

What is point estimation?

Using a sample statistic to estimate a population parameter.
So…
x ̅ = μ
s² = σ²
s = σ
p ̂ = p

What is bias in point estimation?

When any sample statistic, called an ‘estimator’ (θ ̂ ) can be converted to θ, any population parameter, but not just = as above… there is some other factor that influences the result.

What is the bias in point estimation for the estimator in general?

Where an unbiased estimator satisfies b(θ ̂ ) = 0…
b(θ ̂ ) = E(θ ̂ ) - θ

What is the variance of an estimator?

The amount of divergence from the estimator mean.
V(θ ̂ ) = E[(θ ̂ - E(θ ̂ ))²]

What is interval estimation?

Estimation of the amount of variability in any sample statistic when samples are repeatedly taken from a population. Variability can tell us how good that sample statistic actually is in representing the population parameter it is equivalent to.

What is the interval estimator affected by, and what does this change about the parameter we write as a result?

Sample size, so we give parameters with a ± error.

What is this ± error called?

A confidence interval

What is a confidence interval?

A plausible range of values for a population parameter which quantifies how precise its estimator sample statistic is. The higher the confidence interval, in %, the better.

How do you calculate confidence interval?

point estimate ± (confidence) x (SE)
Where:
- point estimate = a value of the statistic like mean.
- confidence = taken from Z-table depending on sampling distribution of the statistic

What is the equation for confidence interval?

x ̅± z (s/√n)