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
