Math 145

What was a sampling distribution?

Suppose we want to know the *mean* of the deck

- How many cards should we draw?
- How should we draw them?
- Draw that many, then calculate the mean, we'll record this

What *would* the distribution look like?

- This is a sampling distribution for \( \bar{x} \)
- It should look nearly normal (Central limit theorem)
- The mean of the distribution will be \( \mu \)
- The standard deviation will be

\[ \frac{\sigma}{\sqrt{n}} \textrm{ (Standard error)} \]

- Observations independent (\( <10\% \) of population)
- Samples size \( \geq 30 \) (rule of thumb)
- Data not strongly skewed

- What's the formula for a 95% confidence interval for means?
- What's the standard error?
- What's the margin of error?