Statistics Chapter 7

the mean of the sampling distribution is

p

sampling distribution

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

When the sample size n is large, the sampling distribution of p^ is close to a Normal distribution with mean p and standard deviation square root of p(1-p) /h.

In practice, use this Normal approximation when both np>or equal to 10 (the Normal condition)

Mean & Standard Deviation of the Sampling Distribution of Sample Means

Suppose that x bar is the mean of an SRS of size n drawn from a large population with mean μ and standard deviation σ. Then: the mean of the sampling distribution of x bar is μ of x bar equals μ.

Central Limit Theorem

The central limit theorem says that when n is large, the sampling distribution of the sample mean x bar is approximately Normal.

The standard deviation of the sampling distribution of ^p is square root of p(1-p)/n for an SRS of size n. This formula can be used if the population is at least 10 times as large as the sample (the 10% condition)

The standard deviation of ^p gets smaller as the sample size n gets larger. Because of the square root, a sample four times larger is needed to cut the standard deviation in half.

parameter

a number that describes the population. a fixed number, but we don't know its value because we cannot examine the entire population

statistic

a number that describes the sample. the value of a statistic is known when we have taken a sample, but it can change from sample to sample. we often use a statistic to estimate an unknown parameter.

unbiased statistic

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

The standard deviation of the sampling distribution of x bar is:

as long as the 10% condition is satisfied. n is greater than or equal to 1/10N, true no matter what shape the population distribution has

variability of a statistic

described by the spread of its sampling distribution. this spread is determined by the sampling design and the size of the sample. larger sample=smaller spread. as long as the pop>sample, spread=approx. the same for any pop size.

sampling distribution of p hat

describes how the statistic varies in all possible samples from the population

mean of the sampling distribution

equal to the population proportion p.