- 180 Views
- Uploaded on
- Presentation posted in: General

Section 12.1 Inference for a Population Proportion

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Section 12.1Inference for a Population Proportion

AP Statistics

Parameters

Mean

µ

Standard Deviation

σ

Proportion

p

Statistics

Mean

x-bar

Standard Deviation

s

Proportion

p-hat

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

3: Calculations

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

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

- 12.5-12.19 odd

AP Statistics, Section 12.1