1. Section 12.1 Inference for a Population Proportion
AP Statistics

2. Parameters vs Statistics
Mean
Standard Deviation σ
Proportion p
Statistics
Mean
x-bar
Standard Deviation s
Proportion
p-hat
AP Statistics, Section 12.1

3. What we know about inference
We are trying to make sense about what is happening at the population level by looking at sample data
Step 1: “What is the population and the parameter of interest?”
We make assumptions in the form of H0
Step 1: “What is H0?”
We need to know about the distribution of the sample statistic
Step 2: “Is the distribution of sample means normal?”
AP Statistics, Section 12.1

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

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

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

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

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

9. 1: Population, Parameter of Interest, H0 and Ha 3: Calculations
2: Procedure Name & Conditions
4: Interpret
AP Statistics, Section 12.1

10. Confidence Intervals
AP Statistics, Section 12.1

11. Calculate the Confidence Interval
1: Population & Parameter of Interest
3: Calculations
2: Procedure Name & Conditions
4: Interpret
AP Statistics, Section 12.1

12. Choosing a sample size We get p* by using previous studies. Or
We use p*=.5 because this is the most conservative choice.
AP Statistics, Section 12.1

13. 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.
AP Statistics, Section 12.1

14. Exercises
odd
AP Statistics, Section 12.1