AP Statistics - Unit 7 - Sampling Distributions

parameter

a number that describes some characteristic of the population

Ex. 83% of all the students in the school prefer Welch’s

statistic

a number that describes some characteristic of a sample

Ex. 60% of the 5 sampled students from the school prefer Welch’s

sampling variability

the fact that the value of a statistic varies in repeated random sampling; decreases as the sampling size increases

Ex. Two different random samplings of 5 students from the school may have two different proportions of students who prefer Welch’s, but that difference is less with samples of 20 students

sampling distribution

distribution of values taken by the statistic IN ALL POSSIBLE SAMPLES of the same size from the same population

Ex. the distribution of the proportions of students who prefer Welch’s in all the possible samples of 5 students from the school

unbiased estimator

a statistic used to estimate a parameter if the mean of its sampling distribution is equal to the value of the parameter being estimated

Ex. the average proportion of students who prefer Welch’s of all the samples of 5 (0.82) is very close to the actual proportion of students in the school who prefer Welch’s (0.83)

sampling variance

the same as normal variance but calculated with n-1 for a sample

variability of a statistic

determined by the spread of its sampling distribution, which is determined mainly by the size of the random sample

sampling distribution of p(hat)

describes how the sample proportion varies in all possible samples from the population

10% condition

10n

central limit theorem

when n is large (n>30), the sampling distribution of x(Bar) is approximately normal

large counts condition

np>10 and n(p-1)>10 in order to approximate to normal