Lecture 3: The Sampling Distribution

Question 1

Central limit theorem

Answer 1

As the number of samples increases, the sampling distribution approaches a normal distribution.

The samples must be large enough before this is the case (typically > 30)

Question 2

The standard error

Answer 2

Tells us how wrong we are on average. When we estimate the mean of a sample using the mean of the population, how wrong are we on average?

The smaller SE is, the more accurate our guesses are.

We calculate the standard error by using the formula SEµ = σ / √N

Question 3

Confidence interval

Answer 3

Window of uncertainty around estimate. We can never be sure that a confidence interval contains the population value, but 95% of confidence intervals ought to include the population value.