Statistics and Probability

Chapter 9 Outline

Chapter 9

A. Sampling Distributions

a. Parameter vs. Statistic

i. Parameter is associated with Population and a

Statistic is associated with a Sample

ii. A statistics is usually extracted to estimate a

parameter for some population.

b. Sampling Variability

i. The effects of the Sampling Variability

1. Take a large number of samples from the same

population

2. Calculate the sample average or proportion for

each sample

3. Make a histogram for the sample means

4. Examine the distribution

ii. Things to notice about the Sampling

Variability of Sample Means

1. Takes on a normal shape

2. Variability is less when n is large

c. Biased Statistic

i.  A description of a sample average or proportion

that may be different from the norm

ii. The goal of any sample is to be low bias and low

variability

B. Sample Proportions

a. Sampling distribution of p-hat

i. When samples from a population is taken and the

proportion is calculated, then the mean of the

population proportion is “p”

ii. The standard deviation of the sampling distribution

is the square root of p times q divided by n

b. Rules of Thumb

i. The population must be 10 times or more larger

than the sample

ii. Np and nq must be larger than or equal to 10

c. Distribution of p-hat

i. If the rules of thumb have been held then the

shape of the distribution is normal

C. Sample Means

a. When samples of size n is taken, and it is unbiased,

it could be assumed that the sample mean will be

the population mean.

b. The standard deviation is the standard deviation of

the population divided by the square root of n

c. The sampling distribution will be close to normal with

the mean and standard deviation stated above.

d. Central Limit Theorem

i. When an SRS of size n is gathered from some

population that is large, the distribution will be

close to normal.  The mean will be close to the

sample mean and the standard deviation will be

the population standard deviation divided by the

sqrt of n.

ii. It doesn’t matter about the actual population

distribution, the distribution of the sample means

will become normal.

AP Statistics

Syllabus

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