Handout 11B: Wrapping Up (Standard error, t-distribution, degree of freedom, finite population correction factor, continuity correction)

What is the formula for the sample variance?

Used to compute Var[Xbar] when we don’t know true standard deviation

What is standard error formula? (using sample standard deviation)

Sample standard deviation is based on estimates of xbar → instead of true standard deviation

• when don’t know the sample standard deviation

• This is called standard error

What is the t-distribution & degree of freedom?

Applies to the standardized sample mean → use when the sample size is small & population standard deviation is unknown!

• very similar to the z-score (instead of standard deviation, use the standard error!)

• dependent on degrees of freedom

• dof = n - 1

What is the finite population correction factor (FPCF) used for & conditions?

When the standard deviation require adjustment

• only applies when sampling WITHOUT replacement (if sampling with replacement, ignore!) → can invoke CLT & it follows a normal distribution

• in n < 10% of population, ignore FPCF

• if sample n > N/10, consider FPCF

• better to do it just in case

What is the finite population correction factor (FPCF) formula?

How do you use the finite population correction factor (FPCF)?

Just multiply it with the sample standard deviation!

• acts as a multiplier that adjusts

When do you use the continuity correction?

• Only useful for area question

• use when n is really large / a lot of calculation is needed

• using a normal model (continuous probability model) to approximate binomial (discrete)

• when the approximation is inaccurate

What is the continuity correction?

The z-score formula + 0.5 in the numerator

When do you add or subtract the continuity correction?

Add: Pr[x < b]
Subtract: Pr[x > a]

How can you adjust/reframe the question to ensure you always add the continuity correction?