Chapter 18 Inference about a Population Proportion

16
1 Chapter 18 Inference about a Population Proportion

description

Chapter 18 Inference about a Population Proportion. Outline. The sample proportion The sampling distribution of Conditions for inference Large-sample confidence intervals for a population proportion Choosing the sample size Significance tests for a proportion. “ p-hat”. - PowerPoint PPT Presentation

Transcript of Chapter 18 Inference about a Population Proportion

Page 1: Chapter 18 Inference about a Population Proportion

1

Chapter 18

Inference about a Population Proportion

Page 2: Chapter 18 Inference about a Population Proportion

2

Outline

The sample proportion The sampling distribution of Conditions for inference Large-sample confidence intervals for a

population proportion Choosing the sample size Significance tests for a proportion

Page 3: Chapter 18 Inference about a Population Proportion

3

1. The Sample proportion p̂

The proportion of a population that has some outcome (“success”) is p.

The proportion of successes in a sample is measured by the sample proportion:

sample the in nsobservatio of count totalsample the in successes of countp̂

“p-hat”

Page 4: Chapter 18 Inference about a Population Proportion

4

2. The sampling distribution of p̂

Page 5: Chapter 18 Inference about a Population Proportion

5

Page 6: Chapter 18 Inference about a Population Proportion

6

3. Conditions for inference

Page 7: Chapter 18 Inference about a Population Proportion

7

Standard Error of

Since the population proportion p is unknown, the standard deviation of the sample proportion will need to be estimated by substituting for p.

ˆ p

n

pps

n

p)-p(1 s.d.

ˆˆ..

1e

Page 8: Chapter 18 Inference about a Population Proportion

8

4. Large-sample confidence intervals for a population proportion

Page 9: Chapter 18 Inference about a Population Proportion

9

Examples

Example 18.4 Estimating risky behavior (Page 476)

Example 18.5 Are the conditions met? (Page 476)

Exercise 18.8 No confidence interval. (Page 477)

Page 10: Chapter 18 Inference about a Population Proportion

10

5. Accurate C.I. for a proportion

Example 18.6 (P479) Shaq’s free shows

Page 11: Chapter 18 Inference about a Population Proportion

11

6. Choosing the sample size

The margin of error in our confidence interval is

We may like to choose the sample size n to achieve a certain margin of error.

n

ppzm

)ˆ1(ˆ*

Page 12: Chapter 18 Inference about a Population Proportion

12

The sample size

Page 13: Chapter 18 Inference about a Population Proportion

13

Guess the sample proportion:

Since we don’t know prior to sampling, we will have to use a guess p* for . There are two ways to do this:

– Use a guess p* based on a pilot study or on past experience.

– Use p*=0.50 as the guess. This guess is conservative, as it gives a margin of error bigger than the true margin of error. (Conservative)

p̂p̂

Page 14: Chapter 18 Inference about a Population Proportion

14

Example

Example 18.7 Planning a poll

(Page 482)

Page 15: Chapter 18 Inference about a Population Proportion

15

7. Significance tests for a proportion

Page 16: Chapter 18 Inference about a Population Proportion

16

Examples

Example 18.8 Is this coin fair?

(Page 484)

Example 18.9 Estimating the chance of head (Page 485)