AP®︎ Statistics: Topic 3.4 Flashcards

We are C% confident that the interval from L to U contains the true proportion of the specified population that has the specified characteristic

If many random samples of the same size were taken from the population and a C% confidence interval were calculated each time by the same method, about C% of those intervals would contain the true population proportion

Not that this particular interval has C% probability of containing p, not that C% of the population has the characteristic or lies in the interval, and not that p̂ has a C% chance of being correct

Values of p inside the interval are reasonably compatible with the sample data and method; values outside are not reasonably compatible at that confidence level

If p₀ is inside the interval, it is a plausible value and the interval does not provide convincing evidence that p differs from p₀; if p₀ is outside, the interval provides convincing evidence that p differs from p₀.

If the claimed value p₀ is exactly an endpoint of the interval, treat it as contained in the interval, so it is a boundary case rather than convincing evidence of a difference

Support p > p₀ if the entire interval is above p₀; support p < p₀ if the entire interval is below p₀; if the interval contains or crosses p₀, there is not convincing evidence for either strict direction

Say the interval provides convincing evidence or supports a claim, not that it proves the claim is true with certainty

Width = U - L = 2(MOE), so the margin of error is half the width of the confidence interval

For the same sample, higher confidence level → larger z* → larger margin of error → wider confidence interval

Greater confidence gives a wider interval and therefore less precision

For a fixed confidence level and roughly the same p̂, larger n → smaller standard error → smaller margin of error → narrower confidence interval

For a given confidence level, confidence-interval width is approximately proportional to 1/√n

The conclusion applies only to the population the sample represents; do not generalize beyond the sampled population or time without justification