AP Stats Chapter 8- Confidence Intervals

Logic of confidence intervals

"95% of samples will be within 2SD of μ"

Template for interpreting confidence intervals

"I am ... % confident that the true ... is between ... and ... ."

Interpreting a confidence level

"If we constructed many intervals in exactly the same manner, about ... % of them will capture the true ... ."

Stay away from saying...

...the word probability after a sample has been taken and calculated.

Two things to remember when constructing and interpreting confidence intervals

1. All data is assumed to be from an SRS because stratified and clustered samples require higher formulas and functions 2. Margin of error simply refers to the variation and does not necessarily mean that someone made a mistake

Example of confidence level

95%

Confidence interval

A set of plausible values for an unknown parameter

Why a point estimate is called a point estimate

Because it is a single point, not a range

Differences between confidence interval and confidence level

Confidence level is more general and starts with "if we created..." whereas confidence interval is done after the fact, after the interval has been created, and includes a specific interval as well as the confidence rating.

Point estimate

Single best guess statistic of a μ or xbar

Formula for calculating confidence interval

Statistic (+-) critical value x standard deviation of statistic

Margin of error

The variation of the sample proportion

Why to include margin of error

To maintain honesty, accuracy and accountability