1. 1 Chapter 18 Inference about a Population Proportion

2. 2 Outline The sample proportion The sampling distribution of Conditions for inference Large-sample confidence intervals for a population proportion Choosing the sample size Significance tests for a proportion

3. 3 1. The Sample proportion The proportion of a population that has some outcome (“success”) is p. The proportion of successes in a sample is measured by the sample proportion: “p-hat”

4. 4 2. The sampling distribution of

5. 5

6. 6 3. Conditions for inference

7. 7 Standard Error of Since the population proportion p is unknown, the standard deviation of the sample proportion will need to be estimated by substituting for p.

8. 8 4. Large-sample confidence intervals for a population proportion

9. 9 Examples Example 18.4 Estimating risky behavior (Page 476) Example 18.5 Are the conditions met? (Page 476) Exercise 18.8 No confidence interval. (Page 477)

10. 10 5. Accurate C.I. for a proportion Example 18.6 (P479) Shaq’s free shows

11. 11 6. Choosing the sample size The margin of error in our confidence interval is We may like to choose the sample size n to achieve a certain margin of error.

12. 12 The sample size

13. 13 Guess the sample proportion: Since we don’t know prior to sampling, we will have to use a guess p* for. There are two ways to do this: –Use a guess p* based on a pilot study or on past experience. –Use p*=0.50 as the guess. This guess is conservative, as it gives a margin of error bigger than the true margin of error. (Conservative)

14. 14 Example Example 18.7 Planning a poll (Page 482)

15. 15 7. Significance tests for a proportion

16. 16 Examples Example 18.8 Is this coin fair? (Page 484) Example 18.9 Estimating the chance of head (Page 485)