18 terms

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