# 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?