Statistical Confidence - Means

Math 145

Reminder

What was a sampling distribution?

Let's consider a deck of cards - again

Suppose we want to know the mean of the deck

Grab A Deck

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

Let's draw the distribution

What would the distribution look like?

What do we get

  • 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

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

Assumptions

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

Confidence interval

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