Chapter 18 Sampling Distribution Models

1. Chapter 18Sampling Distribution Models **Modeling the Distribution of Sample Proportions**

2. Sampling Distribution Modelfor Proportions • We can model the distribution of sample proportions with the Normal Model!! • The mean of sample proportions is the proportion of the population • The standard deviation is

3. Assumptions and Conditions • Before using the normal model to describe the distribution of sample proportions you need: • The sample values must be independent of each other • The sample size, n, must be large enough Check: • Randomization Condition • 10% Condition • Success/Failure Conditions

4. You want to poll a random sample of 100 students on campus to see if they are in favor of the proposed location for the new student center. Of course, you’ll get just one number, your sample proportion. But if you imagined all the possible samples of 100 students you could draw and imagined the histogram all the sample proportions from these samples, what shape would it have? Where would the center of that histogram be? If you think that about half are in favor of the plan, what would the standard deviation of the sample proportions be?

5. Example: Working with sampling distribution models for proportions Suppose that about 13% of the population is left-handed. A 200-seat school auditorium has been built with 15 lefty desks. In a class of 90 students, what’s the probability that there will not be enough seats for the left-handed students?