1. CHAPTER 8 ESTIMATING WITH CONFIDENCE 8.2 Estimating a Population Proportion Outcome: I will state and check all necessary conditions for constructing a confidence interval, determine critical values for calculating a C% confidence interval, construct and interpret a confidence interval for a population proportion and determine the sample size necessary to obtain a C% confidence interval with a specified margin of error.

2. Goldfish Activity! ■s■s

3. Conditions for Estimating p ■Random: The data should come from a well-designed random sample or randomized experiment. –Introduces chance into the data production process –Helps us draw conclusions

4. Constructing a Confidence Interval for p

5. Finding a Critical Value ■If the Large Counts condition is met, we can use a Normal curve. ■To find confidence level C confidence interval, we need to catch the central area C under the Normal curve. ■To find a 95% confidence interval, we used a critical value of 2 based on the 68-95-99.7 Rule. ■Using Table A or a calculator, we can get a more accurate critical value. ■Note: the critical value, z* is actually 1.96 for a 95% confidence level.

6. Example: Finding a Critical Value Use Table A or a calculator to find the critical value z* for an 80% confidence interval. Assume that the Large Counts condition is met. Since we want to capture the central 80% of the standard Normal distribution, we leave out 20%, or 10% in each tail. Search Table A to find the point z* with area 0.1 to its left. So, the critical value z* for an 80% confidence interval is z* = 1.28. The closest entry is z = – 1.28. z.07.08.09 – 1.3.0853.0838.0823 – 1.2.1020.1003.0985 – 1.1.1210.1190.1170

7. One Sample z Interval For A Population Proportion

8. Example: Goldfish ■Suppose you got 107 white goldfish and 144 orange goldfish. Calculate and interpret a 90% confidence interval for p. ■I claim that 50% of the goldfish are white. Use your result from above to comment on this claim.

9. The Four Step Process ■STATE: What parameter do you want to estimate, and at what confidence interval? ■PLAN: Identify the appropriate inference method. Check conditions. ■DO: If the conditions are met, perform calculations. ■CONCLUDE: Interpret your interval in the context of the problem.

10. ■Of a free-response question asks you to construct and interpret a confidence interval, you are expected to complete the four-step process! ■Also, if you use the calculator to compute your interval, you MUST name the procedure you use: ex. One-proportion z interval) and give the interval

11. Calculator! ■STAT  TESTS  A: 1-PropZInt

12. Choosing Your Sample Size

13. Example ■Supposed that you want to estimate p = the true proportion of students at A-High who have a tattoo with 95% confidence and a margin of error of no more than 0.10. ■Determine how many students should be surveyed to estimate p within 0.10 with 95% confidence.