Confidence Interval: a plausible range of values for a population parameter.
Construction of a CI
\[ \textrm{point estimate} \pm \textrm{margin of error} \]
If the distribution of the point estimate can be well approximated by the Normal:
\[ \textrm{point estimate} \pm 1.96 \times SE \]
- point estimate: \(\hat{p}\), \(\bar{x}\)
- standard error (SE): standard deviation of the sampling distribution.
Question
"The proportion of Americans who want to maintain planned parenthood is estimated to be between 39.8% and 58.2% with 95% confidence." Which of the following interpretations are reasonable?
- The interval [.398, .582] provides a plausible range for \(\hat{p}\)
- We are certain that the population proportion lies within this interval.
- If we took many more samples of the same size and computed many \(\hat{p}\)s and many CIs, around 95% of those CIs would contain the population proportion.
