Ch 7: Sampling Distributions

x bar (the sample mean)

estimates μ (the population mean)

p hat (the sample proportion)

estimates p (the population proportion)

Sx (the sample st. dev.)

estimates σ (the population st. dev.

statistic

describes characteristics of a sample

parameter

describes characteristics of a population

sampling variability

different random samples of the same size from the same population product different values for a statistic

sampling distribution

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

unbiased estimator

mean of the sampling distribution is equal to the value of the parameter being estimated

variability

described by the spread of its sampling distribution — inversely proportional to sample size

 sampling distribution of the sample proportion p hat

describes the distribution of values taken by the sample proportion p hat in all possible samples of the same size from the same population. 

mean of the sampling distribution

standard deviation of the sampling distribution (as long as the 10% condition is satisfied)

sampling distribution is approximately Normal if

the Large Counts condition is satisfied

mean of the sampling distribution of p1-p2

standard deviation of p1-p2 if the 10% condition is met

shape of the sampling distribution of p1-p2 is approximately Normal if

the Large Counts condition is met for BOTH samples

sampling distribution of the sample mean x-bar

distribution of values taken by the sample mean x-bar in all possible samples of the same size from the same population

mean of the sampling distribution of x-bar

standard deviation of the sampling distribution of x-bar as long as the 10% condition is met

central limit theorem

when n is sufficiently large (> or =30), the sampling distribution of the sample mean xis approximately Normal.

mean of the sampling distribution of x1-x2

standard deviation of the sampling distribution of x1-x2 as long as the 20% condition is met

the shape of the sampling distribution of x1-x2 is Normal if

both populations are normal OR if the CLT is satisfied