Interval → A lower and upper limit

Confidence level → Probability that the interval contains mu

How far are most sample means from the true population mean mu ?

To know this we need to define three variable

• Margin of error
• Confidence level
• Significance level

Margin of error:

1. The distance on either side of the population mean (mu).

Confidence level:

1. Probability that your sample mean is within the margin of error

2. Probability that a randomly generate sample mean is within the margin of error

3. Probability a confidence interval contains mu

$$ \text{Confidence Level} = 1 - \alpha \\

$$

For a 95% confidence level:

$$ \alpha = 0.05 \\\text{Confidence Level} = 1 - \alpha = 0.95 $$

Confidence Interval: