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Section 12.1 Inference for a Population ProportionPowerPoint Presentation

Section 12.1 Inference for a Population Proportion

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### Section 12.1Inference for a Population Proportion

AP Statistics

Mean

µ

Standard Deviation

σ

Proportion

p

Statistics

Mean

x-bar

Standard Deviation

s

Proportion

p-hat

Parameters vs StatisticsAP Statistics, Section 12.1

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

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

But what about proportions?

- We learned in Chapter 9 about the distribution of sample proportions.

AP Statistics, Section 12.1

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

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

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

1: Population, Parameter of Interest, H0 and Ha

2: Procedure Name & Conditions

4: Interpret

AP Statistics, Section 12.1

Confidence Intervals

AP Statistics, Section 12.1

Calculate the Confidence Interval

3: Calculations

1: Population & Parameter of Interest

2: Procedure Name & Conditions

4: Interpret

AP Statistics, Section 12.1

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

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.

ExampleAP Statistics, Section 12.1

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