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# Section 12.1 Inference for a Population Proportion - PowerPoint PPT Presentation

Section 12.1 Inference for a Population Proportion. AP Statistics. Parameters Mean µ Standard Deviation σ Proportion p. Statistics Mean x-bar Standard Deviation s Proportion p-hat. Parameters vs Statistics. What we know about inference.

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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 Statistics

AP Statistics, Section 12.1

• 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

• Has been about the distribution of sample means

• and the distribution of the difference of sample means.

AP Statistics, Section 12.1

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

AP Statistics, Section 12.1

• 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

• 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

• 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

AP Statistics, Section 12.1

3: Calculations

1: Population & Parameter of Interest

2: Procedure Name & Conditions

4: Interpret

AP Statistics, Section 12.1

• We get p* by using previous studies.

• Or

• We use p*=.5 because this is the most conservative choice.

AP Statistics, Section 12.1

How large of a sample is needed to get the ME of a 95% CI below 5%?