1. Chapter 9: Means and Proportions as Random Variables 9.1 Understanding dissimilarity among samples 9.2 Sampling distributions for sample proportions 9.3 What to expect of sample means 9.4 What to expect in other situations: Central Limit Theorem Etc.

2. Chapter 9 dependencies

3. 9.1 Understanding dissimilarity among samples Suppose we have a population with known characteristics (as in your lab). We propose to pick a random sample from this population. The science of probability can describe for us the random behavior of this sample.

4. 9.1 cont’d: “Statistics is Probability in reverse” On the other hand, if we have a population with unknown properties, suppose we select a sample at random. In Statistics, we use certain characteristics (statistics) of the sample to learn about the properties (parameters) of the population. Probability: Describe sample behavior from population characteristics. Statistics: Infer population behavior from sample characteristics by applying probability logic in reverse.

5. Probability Statement:

6. Statistics Statement:

7. 9.2 An example involving proportions Recent studies have shown that about 20% of American adults fit the medical definition of being obese. A large medical clinic would like to estimate what percent of its patients is obese, so it takes a random sample of 100 patients and finds that 18 are obese. Suppose that in truth, the same percent holds for the patients of the medical clinic as for the general population, 20%. (Problem 9.11, page 281)