Day 16 AGENDA: DG #9 --- 15 min Unit 1 Test #1 Tues Tues’ Agenda:

Lesson #13: Confidence Intervals For Proportions Accel Precalc Unit #1: Data Analysis Lesson #13: Confidence Intervals For Proportions EQ: How do you use confidence intervals to estimate population means and proportions?

s  p  Mean Standard Deviation Proportion p-hat --- sample proportion RECALL (AGAIN): Examples of: Statistics Parameters  Mean s  Standard Deviation New Notation: Statistics Parameters p Proportion p-hat --- sample proportion p --- population proportion p-hat is used as an estimator for p

General Formula: Confidence Interval for Proportions: X = # of successes n = # in sample or General Formula: Confidence Interval for Proportions: Since we are back to using a Normal Distribution (z -values) we do not have to worry about df’s.

RECALL: 90% 95% 99% Common Confidence Intervals: See Table C for critical values. Which value will you use for confidence intervals for proportions? 1.96 2.576 90% ______ 95% ______ 99% _______ 1.645 For Confidence Intervals for Proportions you will always use the LAST ROW of the t-distribution table.

We are ______% confident that the true population proportion of Confidence Interval Statement: We are ______% confident that the true population proportion of __________[in context of problem] will be between ____% and ____%.

HINT: Mr. T was a “MEAN” dude!! z-distributions proportions t-distributions means Mr. T was a “MEAN” dude!!

In Class Examples 1. In recent survey of 150 households, 54 had central air conditioning. Find p-hat and q-hat, where p-hat is the proportion of households that have central air conditioning.

A sample of 500 nursing applications included 60 from men A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

We are ______% confident that the true population proportion of Confidence Interval Statement: We are ______% confident that the true population proportion of ___________ will be between ____% and ____% . 90 men who applied to the nursing program 14.4 9.6

3. A survey of 200,000 boat owners found that 12% of the pleasure boats are named Serenity. Find the 95% confidence interval of the true proportion of boats named Serenity.

We are ______% confident that the true population proportion of Confidence Interval Statement: 95 We are ______% confident that the true population proportion of ___________ will be between ____% and ____%. pleasure boats named Serenity 11.86 12.14

4. A U.S. Travel Data Center’s survey of 1500 adults found that 42% of respondents stated that they favor historical sites as vacations. Find the 95% confidence interval of the true proportion of all adults who favor visiting historical sites as vacations.

We are ______% confident that the true population proportion of Confidence Interval Statement: We are ______% confident that the true population proportion of ___________ will be between ____% and ____% . 95 respondents stated…vacations 39.5 44.5

5. In a survey of 1004 individuals, 442 felt that President George W 5. In a survey of 1004 individuals, 442 felt that President George W. Bush spent too much time away from Washington while he was in office. Find a 95% confidence interval for the true population proportion who felt Bush spent too much time away from Washington while he was in office . n = 1,004 x = 442 CL = 95% z* = 1.96 0.44 ± 0.0307 (0.4093, 0.4707)

We are ______% confident that the true population proportion of Confidence Interval Statement: We are ______% confident that the true population proportion of ___________ will be between ____% and ____% . 95 individuals who felt…from Washington 40.93 47.07

6. In a recent study of 75 people, 41 said they were dissatisfied with their community’s snow removal service. Find the 95% confidence interval of the true proportion of individuals who are dissatisfied.

6. In a recent study of 75 people, 41 said they were dissatisfied with their community’s snow removal service. Find the 95% confidence interval of the true proportion of individuals who are dissatisfied. n = 75 x = 41 CL = 95% z* = 1.96 0.55 ± 0.1126 (0.4374, 0.6626)

We are ______% confident that the true population proportion of Confidence Interval Statement: We are ______% confident that the true population proportion of ___________ will be between ____% and ____% . 95 respondents stated…removal service 43.74 66.26

Assignment: Practice Worksheet: Confidence Intervals for Proportions More Practice: CLT & Confidence Intervals Tues’ Agenda: