18 terms

AP Statistics: 8.1 // Confidence Intervals

STUDY
PLAY
point estimator
statistic - provides an estimate of population parameter
point estimate
value of that statistic from a sample - best guess at value of unknown parameter
for population mean use ? as point estimator
sample mean
for population variance SD^2 use ? as point estimator
sample variance s²x
confidence interval
(for a parameter) = estimate ± margin of error
margin of error
how close estimate tends to be to unknown parameter in repeated random sampling
confidence level C
gives overall success rate of method for calc confidence interval → in C% of all possible samples, the method would yield an interval that captures the true parameter value
95% confident
95% of all possible samples of given size from this pop → will result in an interval that captures the unknown parameter
C% confidence interval
we are C% confident that the interval from ∼ to ∼ captures the actual value of the [population parameter]
is confidence level chance?
no - it gives us a set of plausible/reasonable values for the parameter
what's the probability that our 95% confidence interval captures the parameter?
NOT 95% → mean(randNorm) → resulting confidence interval = either does/not contain population mean
interpret the confidence interval -- 95% confidence interval = (0.167, 0.213)
confidence interval = we are 95% confident that the interval from 0.167 to 0.213 contains the actual proportion p of US adults who use Twitter/others
interpret the confidence level -- 95% confidence interval = (0.167, 0.213)
confidence level = in 95% of all possible samples of 2253 US adults, the resulting c.i. would capture the actual population proportion of Us adults who use Twitter/others
critical value
sets a finite value - so you know when to reject ---- advantage = define rejection region in terms of sample mean & make conclusion in field you are collecting ---- disadvantage = stuck w/ fixed level for the test
confidence interval calculation
statistic ± (critical value) × (SD of statistic)
ME formula
(critical value) × (SD of statistic)
when does ME get smaller?
confidence level decreases & sample size n increases
3 conditions to check before calc C.I.
1) Random → 2) Normal - means = at least 30; proportions = at least 10 → 3) Independent - sample size < 10% N