Warm-up8.1 Day 2 Notes

Answers to D1, D2-D3D1: 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 is44.8% to 75.2%. It is reasonably likely that 27 from the 40Hispanic 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 theconfidence 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 precisecritical 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 ourconfidence 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 votersfound 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.

n

ppzp

)1(ˆ *

Problem 2 using 1-PropZIntIn May 2006, the Gallup Poll, randomly asked 510 randomlysampled adults the question “Generally speaking, do youbelieve the death penalty is applied fairly or unfairly in thiscountry 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 sampleFox News estimated that 82% of all voters believe globalwarming exists.Suppose an environment group plans a follow-up survey ofvoter’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?

n

ppzME

)1(*

Inference for Distributions

p̂ m x mx m*

ˆˆ pp z SE *xx z SE *

xx t SE

* ˆ ˆ(1 )ˆ

p pp z

n

*x zn

* s

x tn

Confidence Intervals

8.2 Testing a Proportion 9.1 Confidence Interval of the Mean 9.2 Significance Testing for the Mean

H.W. from 8.1For Statistics: E #11-14

A.P. Statistics: E#11-14 and 16