Download Chapter 20: Confidence Intervals for proportions

Chapter 20: Confidence Intervals for proportions
A confidence interval is simply a interval; constructed with some level of
confidence in capturing some unknown, but fixed, population parameter.
We want to estimate some unknown population parameter.
E.G.
1. (Applies to Ch20) Gallup estimating the true proportion of Americans 18+
who believes that Global Warming concept is exaggerated.
2. (Applies to Ch20) We used our class survey to estimate true proportion of
PUS students who have made out with someone of the same gender.
3. (Applies to Ch21) We used call survey to estimate (mean) money spent
on textbooks.
P-value is the probability of obtaining a result at least as extreme as the one that
was actually observed, assuming that the null hypothesis is true.
Population Parameters (population): unknown, fixed quantity
1. True proportion of 18+ who believe Global Warming exaggerated.
Sample Statistics: quantities from sample used to estimate parameter.
2. Sample proportion of 41%; I.E. the 41% of sample of 1012 who said “yes”
A parameter is a measure of the entire population while a statistic is a measure of the
sample.
Statistic is to Sample as Population is to Parameter.
Notation: P-> population parameter p^ -> sample proportion. We know if the
number in sample with the ”trait of interest”
E.G. Those who said yes, is 25 and the number without trait is less than or
equal to 5 then the SD of proportion  (P^*(1-P^)/ (n). Then 95% ME: 2 times SD.
Gallup poll:
n(sample size)=1012
P^(Sample proportion)= .41
SD(Standard Deviation)=  ((.41)*(1-.41))/ (1012)=.015
95% ME: 2* .015=.03
Class Survey:
n(Sample Size)= 105
P^(Sample proportion)=.19
SD(Standard Deviation)=(.19)*(1-.19)/(105)= .038
95% ME = 2*.038=.076
Basic Confidence Interval Expression:
Sample Statistic +- Multiplier * SD (or SE)
Gallup Poll: p^ +- ME
.41+- 0.03=>.38 to .44
Gallup: Since 95% ME the .38 to .44 is a 95% Confidence Interval for estimating the
true proportion of 18+ Americans who feel global warming exaggerated.
Interpretation: We are 95% confident that the true proportion of Americans 18 and
older who Global Warming is exaggerated is between 38% and 44%.
Class Survey:
n= 105
P^=.19
95% ME= .076
95% C.I.= .19 +- .076= .114 to .266
We are 95% confident that the true proportion of PSU students who have made out
with someone of the same gender is from 11.4% to 26.6%.
Levels of Confidence:
On the Quiz we had
68%: 1*SD to get 68% ME
95%: 2*SD to get 95% ME
99.7%: 3*SD to get 99.7%
68% and 99.7% are not usually used. The three common confidence levels are :
90%
95%
99%
Multiplier
1.65
2
2.58
Interval
Narrow range
Confidence
Less Confident
Wide range
More Confident