Stats SB Notes 6.3 Completed.notebook April 03, Mar 23 5:22 PM. Chapter Outline. 6.1 Confidence Intervals for the Mean (σ Known)

Transcription

1 Stats SB Notes 63 Completednotebook April 03, 2017 Chapter 6 Confidence Intervals Chapter Outline 61 Confidence Intervals for the Mean (σ Known) 62 Confidence Intervals for the Mean (σ Unknown) 63 Confidence Intervals for Population Proportions 64 Confidence Intervals for Variance and Standard Deviation

2 Stats SB Notes 63 Completednotebook April 03, 2017 Section 63 Confidence Intervals for Population Proportions Section 63 Objectives How to find a point estimate for the population proportion How to construct and interpret confidence intervals for a population proportion How to determine the minimum sample size required when estimating a population proportion

3 Stats SB Notes 63 Completednotebook April 03, 2017 Point Estimate for Population p Population Proportion The probability of success in a single trial of a binomial experiment Denoted by p Point Estimate for p The population proportion of successes in a sample Denoted by > > read as p hat Point Estimate for Population p Estimate Population Parameter with Sample Statistic Proportion: p Point Estimate for q, the proportion of failures Denoted by Read as q hat

4 Stats SB Notes 63 Completednotebook April 03, 2017 Example 1 Finding a Point Estimate for p In a survey of 1000 US teens, 372 said that they own smartphones Find a point estimate for the population proportion of US teens who own smartphones Mar 31 8:51 AM Example: Point Estimate for p In a survey of 1000 US adults, 662 said that it is acceptable to check personal e mail while at work Find a point estimate for the population proportion of US adults who say it is acceptable to check personal e mail while at work (Adapted from Liberty Mutual)

5 Stats SB Notes 63 Completednotebook April 03, 2017 Try It Yourself 1, pg 320 In a survey of 2462 US teachers, 123 said that "all or almost all" of the information they find using search engines online is accurate or trustworthy Mar 31 8:52 AM Confidence Intervals for p A c confidence interval for the population proportion p The probability that the confidence interval contains p is c, assuming that the estimation process is repeated a large number of times

6 Stats SB Notes 63 Completednotebook April 03, 2017 Constructing Confidence Intervals for p Constructing Confidence Intervals for p

7 Stats SB Notes 63 Completednotebook April 03, 2017 Example 2 Constructing a Confidence Interval for p Use the data in Example 1 to construct a 95% confidence interval for the population proportion of US teens who own smartphones Mar 31 8:56 AM Example: Confidence Interval for p In a survey of 1000 US adults, 662 said that it is acceptable to check personal e mail while at work Construct a 95% confidence interval for the population proportion of adults in the US adults who say that it is acceptable to check personal e mail while at work

8 Stats SB Notes 63 Completednotebook April 03, 2017 Try It Yourself 2 Use the data in Try It Yourself 1 to construct a 90% confidence interval for the population proportion of US teacher who say that "all or almost all" of the information they find using search engines online is accurate or trustworthy Mar 31 8:56 AM Example 3 Construct a Confidence Interval for P In a survey of 498 US adults, 71% said teenagers are the most dangerous drivers, 25% said people of 65, and 4% had no opinion Construct a 99% confidence interval for the population proportion of US adults who think that teenagers are the more dangerous drivers Mar 31 8:59 AM

9 Stats SB Notes 63 Completednotebook April 03, 2017 Try It Yourself 3, pg 323 Use the data from Example 3 to construct a 99% confidence interval for the population proportion of adults who think that people over 65 are the more dangerous drivers Mar 31 9:01 AM Determining a Minimum Sample Size Given a c confidence level and a margin of error E, the minimum sample size n needed to estimate p is This formula assumes you have an estimate for and If not, use and

10 Stats SB Notes 63 Completednotebook April 03, 2017 Example: Sample Size You are running a political campaign and wish to estimate, with 95% confidence, the proportion of registered voters who will vote for your candidate Your estimate must be accurate within 3% of the true population Find the minimum sample size needed if no preliminary estimate is available Example: Determining a Minimum Sample Size You are running a political campaign and wish to estimate, with 95% confidence, the proportion of registered voters who will vote for your candidate Your estimate must be accurate within 3% of the true population Find the minimum sample size needed if a preliminary estimate gives

11 Stats SB Notes 63 Completednotebook April 03, 2017 Try It Yourself 4, pg 324 A researcher is estimating the population proportion of US adults ages 18 to 24 who have had an HIV test The estimate must be accurate within 2% of the population proportion with 90% confidence Find the minimum sample size needed when (1) no preliminary estimate is available and (2) a previous survey found that 31% of US adults ages 18 to 24 have had an HIV test HW Stats Section 63 pg 325, 1-20, Evens