1. 9.1: What Is a Confidence Interval? Statistics Chap 9:Introduction to Inference

2. Statistics and Parameters

3. Types of Estimates Point Estimate:A single number that is used to estimate an unknown population parameter. Interval Estimate:A range of values used to estimate a population parameter. Describes a range of values within which a population parameter is likely to lie.

4. Estimators and Estimates

5. Youth Risk Behavior Survey The Youth Risk Behavior Surveillance System (YRBSS) monitors six types of health-risk behaviors that contribute to the leading causes of death and disability among youth and adults, including— Behaviors that contribute to unintentional injuries and violence Sexual behaviors that contribute to unintended pregnancy and sexually transmitted diseases, including HIV infection Alcohol and other drug use Tobacco use Unhealthy dietary behaviors Inadequate physical activity

6. Example: Teen smoking The 2007 Youth Risk Behavior Survey questioned a nationally representative sample of 14,041 students in grades 9 to 12. Of these, 2808 said they had smoked cigarettes at least one day in the past month. Identify: Population: Parameter: Statistic:

7. Confidence Level / Confidence Interval Confidence Level:The probability that we associate with an interval estimate. Confidence Interval:The range of the estimate we are making. In order to attain a high confidence level, we must use a wide confidence interval.

8. Confidence Level / Confidence Interval Suppose we calculate from one sample the following confidence interval and confidence level: “We are 95% confident that the mean battery life of the population lies within 30 and 42 months.” This statement does not mean that the chance is 0.95 that the mean life of all batteries falls within the interval established from a single sample. Instead, it means that if we select many random samples of the same size and if we calculate a confidence interval for each of these samples, then in about 95 % of these cases, the population mean will lie within that interval.

9. Activity 9.1A: Estimating the proportion of brown M&M candies pp 488-490

10. Activity: The Candy Machine

11. Sampling distribution of a sample proportion The distribution of the values taken by the sample proportion in all possible samples of the same size from the same population.

12. Sampling distribution of a sample proportion

14. 68% Confidence Interval for a proportion

15. 95% Confidence Interval for a proportion

16. Example: A confidence interval for youthful smokers

17. Exercises pp 495-496: 9.1, 9.2, 9.5

18. Confidence Interval A level C confidence interval for a parameter has two parts: 1. An interval calculated from the data 2. A confidence level C, which gives the probability that the interval will capture the true parameter value in repeated samples.

19. Activity 9.1B: The Confidence Intervals Applet pp 497-498 http://www.rossmanchance.com/applets/ Simulating Confidence Intervals for Population ParameterSimulating Confidence Intervals for Population Parameter (js)

20. Confidence Interval for a population proportion

21. Example: A 99% confidence interval

22. Confidence Intervals on the Calculator STAT → TESTS → 1-PropZInt X = # of successes n = sample size C-Level = Confidence Level

23. Example: Determining sample size

24. Exercises

25. 9.1 Review Statistical InferenceDraw conclusions about a population on the basis of data from a sample

26. 9.1 Review Exercises pp 508-509: 9.12, 9.14

27. 9.1 Bead Exercise Four containers (labeled I-IV ) contain colored beads. Consider each container a population. Your goal is to estimate the actual proportion of beads in the population that have a particular color. 1.Describe your sampling strategy. 2.Calculate and interpret a 95% CI for the proportion of beads in the population that have the specified color. 3.Is it possible that your CI does not capture the actual population proportion? Explain.

28. 9.1 Bead Exercise III Black.413.267 Gray.253.400 Purple.333 IIIIV Red.240.414 White.360.310 Blue.400.276