1. Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application Due: March 1 st

2. Remember Conditions for Inference  Data are an SRS from the population of interest.  Observations are independent (pop. ≥ 10*n)  Sampling Distribution is approx. normal  Today, we’re dealing with proportions, so np ≥ 10 and n(1- p) ≥ 10.

3. Standard Error

4. Inference for a Population Proportion

5. Remember:  S tate  P lan DoDo  C onclude S tatistics P roblems D emand C onsistency!!!

6. Example 1 A Gallup Poll found that 28% of a SRS of 682 American adults expect to inherit money. Construct a 90% Confidence interval for the true proportion. State: know what parameters we’re estimating & at what confidence level We want to estimate p = the true proportion of US adults who expect to inherit $ with 90% confidence.

7. Example 1 Plan: choose method & check conditions Method: Proportions Conditions: Random: Independent: Normal: Assume Gallup used correct sampling procedures n = 682, the population of adults is much larger than 6820 (pop. ≥ 10*n), so assume independence.

8. Example 1

10. YOUR TURN!!! The New York Times and CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17-year-olds. Of these teenagers, 692 had a television in their room. We will act as if the sample were an SRS. Construct a 95% confidence interval for the proportion of all people in this age group who have a TV in their room.

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12. Choosing the sample size

15. Example 12.9, p. 696  Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. You are planning a sample survey to determine what percent of the voters plan to vote for Chavez. This is a population proportion p. You will contact an SRS of registered voters in the city. You want to estimate p with 95% confidence and a margin of error no greater than 3%, or 0.03. How large a sample do you need?

16. Example 12.9, p. 696 Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. You are planning a sample survey to determine what percent of the voters plan to vote for Chavez. This is a population proportion p. You will contact an SRS of registered voters in the city. You want to estimate p with 95% confidence and a margin of error no greater than 3%, or 0.03. How large a sample do you need? Should we use p * = 0.5? YES!

17. So we need n = 1068 to satisfy this inequality.

18. Homework:  p. 694: 12.8, 12.9  P. 696: 12. 10, 12.11 Due: Tuesday