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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 12.1 Inference for a Population Proportion

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Section 12 1 inference for a population proportion l.jpg

Section 12.1Inference for a Population Proportion

AP Statistics


Parameters vs statistics l.jpg

Parameters

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


What we know about inference l.jpg

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


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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


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But what about proportions?

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

AP Statistics, Section 12.1


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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


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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


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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


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3: Calculations

1: Population, Parameter of Interest,H0 and Ha

2: Procedure Name & Conditions

4: Interpret

AP Statistics, Section 12.1


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Confidence Intervals

AP Statistics, Section 12.1


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Calculate the Confidence Interval

3: Calculations

1: Population & Parameter of Interest

2: Procedure Name & Conditions

4: Interpret

AP Statistics, Section 12.1


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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


Example l.jpg

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.

Example

AP Statistics, Section 12.1


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Exercises

  • 12.5-12.19 odd

AP Statistics, Section 12.1


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