Section 7.1 1

Parameter v. Statistic 2

Example 3

Sampling Variability The value of a statistic varies in repeated random sampling. We will do a penny activity on Monday 4

What would happen if we took many samples? Take a large number of samples from the same population. Calculate the statistic for each sample. Make a graph of the values of the statistic. Examine the distribution displayed in the graph for SOCS. 5

Sampling Distribution The sampling distribution of a statistic is the distribution of the values taken by the statistic in all possible samples of the same size from the same population. 6

Population Distribution The population distribution give the values of the variable for all the individuals in the population. If we would have combined all of the data before finding the mean of our pennies and put them all on one dotplot, we would have made a population distribution. 7

Be careful! Don’t confuse the sampling distribution with a distribution of sample data, which gives the values of the variable for all individuals in a sample. Example – In your groups you made distributions of sample data. As a class, we made a sampling distribution. If we had all of the years of all pennies, that would be a population distribution. 8

Describing Sampling Distributions A statistic used to estimate a parameter is an unbiased estimator or a biased estimator. Bias means that the center (mean) of the sampling distribution is not equal to the true value of the parameter. It is called “unbiased” because in repeated samples, the estimates won’t consistently be too high or too low. It doesn’t mean it will be perfect! 9

Variability of a Statistic The variability of a statistic is described by the spread of its sampling distribution. The spread of the sampling distribution does not depend on the size of the population, as long as the population is at least 10 times larger than the sample. Larger samples give smaller spread. 10

Extra Stuff! When trying to estimate a parameter, choose a statistic with low or no bias and minimum variability. Don’t forget to look at shape of the sampling distribution before doing inference. 11

Homework Pg 428 (5, 6) Pg 439 (31, 36) Pg 459 (54, 56) 12