Section 6.4 Sampling Distributions

2 Population Vs. Sample Population: existing or conceptual set of measurements or counts if we took a census Sample: subset of measurements from the population when we can’t take a census Statistics Parameters

3 Dice Activity : Population Distribution: Samples from the population: Sampling Distribution:

4 Sampling Distributions: Set of a sample statistic calculated from random samples of the same size drawn from the same population

5 Sampling distribution for x Pinedale, Wisconsin, is a rural community with a children’s fishing pond. Posted rules state that all fish under 6 inches must be returned to the pond, only children under 12 years old may fish, and a limit of five fish may be kept per day. As a project for her biometrics class, Susan kept a record of the lengths (to the nearest inch) of all trout caught last summer. Hundreds of children visited the pond and caught their limit of five trout, so Susan has a lot of data. To make Table 6-9, Susan selected 100 children at random and listed the lengths of each of the five trout caught by a child in the sample.

6 Sampling distribution for x

7

8 Let’s organize our values into a frequency table. We used a class width of 0.38 to make: Frequency Table for 100 Values of x Sampling distribution for x

9 Make a relative frequency histogram: Sampling distribution for x

10 Sampling distribution for x 1.What makes up the members of the sample? 2.What is the sample statistic corresponding to each sample? 3.What is the sampling distribution? 4.To which population parameter does this sampling distribution correspond?