AP Statistics: Unit 7

parameter

a number that describes some characteristic of the population

statistic

a number that describes some characteristic of the sample

sampling variability

the value of a statistic varies in repeated random sampling; we need to estimate sampling variability so we know how close our estimates are to the truth (margin of error).

sampling distribution

the distribution of values taken by the statistic in all possible samples of the same size from the same population

distribution

describes possible values and how often they occur

distribution of the population

gives the values of the variable for all individuals in the population

ex. proportion of all pennies minted in 2000s

distribution of sample

shows the values of the variable for the individuals in the sample

ex. proportion of pennies in your individual sample minted in 2000s

sampling distribution of a sample statistic

describes how a statistic varies in many samples from the population

ex. the proportion of pennies minted in 2000s from all samples

unbiased estimator

mean of the sampling distribution of a statistic is equal to the true value of the parameter

what are biased estimators?

range, standard deviation

what are unbiased estimators?

mean, IQR, variance

biased estimator

statistic is consistently higher or lower than the parameter

how can you reduce the variability of a statistic?

bigger sample size

better design (stratified sampling)

what effect does the size of the population have on the variability of a statistic?

not much, as long as the population is at least 10x the sample (10% condition)

what is the difference between accuracy and precision?

accurate = unbiased

precise = low variability

when is it OK to say that the distribution of phat is approximately Normal?

np and n(1-p) are at least 10

sampling distribution of a sample proportion

shape: as n increases, the sampling distribution of sample proportions becomes approximately Normal.

center: µphat = p

spread: σphat = √p(1-p)/n if the 10% rule applies

sampling distribution of a sample mean

µxbar = µ

σxbar = σ/√n, n ≤ 1/10N

what is the shape of the sampling distribution of a sample mean when the sample is taken from a Normally distributed population?

always normal, regardless of size

central limit theorem

for large samples, xbar sampling distribution will be approximately normal; for small samples, it will resemble the shape of the original population.

n ≥ 30