1. Warm Up 1. Write the four steps in writing a confidence interval and how to check conditions (step 2) for means. 2. Write the four steps involved in test of significance for means. AP Statistics, Section 12.1 1

2. Warm Up a) describe the population and parameter. b) Give a numerical value of the statistic p-hat that estimates p. 1. Tonya wants to estimate what proportion of the students in her dormitory that like dorm food. She interviews an SRS of 28 of 175 students living in the dormitory. She finds that 12 think the dorm food is good. 2. Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of 100 of 2400 students at his college. Forty-two of those interviewed think tuition is too high. 2

3. Section 12.1 Inference for a Population Proportion AP Statistics

4. AP Statistics, Section 12.1 4 Parameters vs Statistics Parameters  Mean (True Mean) µ  Standard Deviation σ  Proportion p Statistics  Mean (Sample Mean) -  Standard Deviation s  Proportion -

5. AP Statistics, Section 12.1 5 What we know about inference

6. AP Statistics, Section 12.1 6 Our inferential work so far… Has been about the distribution of sample means and the distribution of the difference of sample means.

7. AP Statistics, Section 12.1 7 But what about proportions? We learned in Chapter 9 about the distribution of sample proportions.

8. AP Statistics, Section 12.1 8 But what about proportions? We know that the distribution of sample proportions is approximately normal when these conditions are met…  np>10  nq>10

9. AP Statistics, Section 12.1 9 Simulation A recent study concluded that 25% of all U.S. teenage females have a STD. Simulate sampling 500 randomly chosen teenage females using…  MATH  PRB  7:randBin( n, prob. of success)  randBin(500,.25) Simulate finding the sample proportion by using…  randBin(500,.25)/500

10. AP Statistics, Section 12.1 *NEW 1: Population and Parameter of Interest 2: Procedure Name & Conditions 3: Calculations 4: Interpret Population: teenage girls. Parameter: proportion with STDs Unbiased? SRS stated Independent? Pop>10n Normal? n p ≥10 n(1- p )≥10 CI= p z* z*=1.96 for 95% confidence interval With ___% confidence we believe the true proportion of teenage females with STDs is between ____ and ___ Calculate the 95% Confidence Interval 1-PropZInt

11. Using the Calculator STAT  TEST  A:1-PropZInt  x- # of success (CANNOT be a decimal)  n-sample size  C-Level AP Statistics, Section 12.1 11

12. AP Statistics, Section 12.1 12 Confidence Intervals Margin of Error

13. AP Statistics, Section 12.1 13 Test of significance A recent sample of 500 female teenagers from southeastern Oakland county found the 22% have an STD. (made up numbers) Is this strong evidence to suggest that teenage females from SE Oakland county have a lower infection rate than the national average of 25%?

14. AP Statistics, Section 12.1 *NEW 2: Procedure Name & Conditions 3: Calculations 4: Interpret Population: teenage girls. Parameter: proportion with STDs Unbiased? SRS not stated PWC Independent? Pop>10n Normal? n p ≥10 n(1- p )≥10 Since our p-value is so high, we fail to reject Ho at the alpha level of 0.05. There is insufficient evidence to suggest that the proportion of teenage females with STDs in SE Oakland county is lower. Significance Test 1: Population, Parameter of Interest, null and alternate hypothesis. Ho: p=.25 Ha: p<.25 p’s has no hat! For significance test. 1prop z-test

15. AP Statistics, Section 12.1 15 Example We believe that 15% of people are left handed. How large of a sample is needed to get the ME of a 95% CI below 5%? Answer: at least 196. Margin of Error

16. AP Statistics, Section 12.1 16 Choosing a sample size (when p-hat isn’t given to you = p*) We get p* by using previous studies. Or We use p*=.5 because this is the most conservative choice.

17. AP Statistics, Section 12.1 17 Exercises 12.5-12.19 odd