Advanced Placement

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


           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



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


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