Warm-up 8.1 Day 2 Notes

Answers to D1, D2-D3 D1: a. 30.8% to 39.2% b. p-hat = 145/500 = 29% so it is not reasonably likely. D3: p-hat = 67.5% The range of reasonably likely events is 44.8% to 75.2%. It is reasonably likely that 27 from the 40 Hispanic surveyed are of Mexican origin. D4: The range of reasonably likely 15.8% to 44.2%, so 60% is not a reasonably likely event. D5: P-hat is 34/40 = 0.85 and the confidence interval is 73.9% to 96.1%. D7: P-hat can be obtained from a sample. The purpose of the confidence interval is to find where the actual p may lie.

8.1 (Day 2) Confidence Intervals and Margin of Error So far we have learned that a 95% confidence interval has a precise critical value of z* = 1.96 and to find the confidence interval we used Z *, the critical value, can change based on the size we want our confidence interval to be. This process is also called a one-proportion z-interval. Problem 1: In January 2007 a Fox news poll of 900 registered voters found that 82% of the respondents believed global warming exists. Fox reported a confidence interval of 90% with a + 2% margin of error. Find the confidence interval and confirm the margin of error.

Problem 2 using 1-PropZInt In May 2006, the Gallup Poll, randomly asked 510 randomly sampled adults the question “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?” Of these; 60% answered “Fairly,” 35% said “Unfairly,” and 5% said they didn’t know. 1)Are the conditions met to perform a one proportion z- interval test? 2)Find the 95% confidence interval for those that believe that the death penalty is applied fairly. *To use the calculator find 60% of 510 first!

Finding the size of a sample Fox News estimated that 82% of all voters believe global warming exists. Suppose an environment group plans a follow-up survey of voter’s opinions on global warming. They want a 95% confidence interval with a margin of error no more than + 2%. How big should their sample be?

Inference for Distributions Sample Proportion Sample Mean (known ) Sample Mean (unknown ) General formula Specific formula Expanded formula Calc Function1-Prop Z IntervalZ intervalT Interval Confidence Intervals 8.2 Testing a Proportion 9.1 Confidence Interval of the Mean 9.2 Significance Testing for the Mean

H.W. from 8.1 For Statistics: E #11-14 A.P. Statistics: E#11-14 and 16