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
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