Friday, January 14
Topic: Confidence Intervals
Topic: Hypothesis Testing
Act: Colors of Reeses' Pieces
Read: Utts 19
Read: Utts 20 (optional)
Read: Utts 21
Due: HW #6 @ hw04.shtml
Vocab: confidence level, confidence interval, margin of error,%%
hypothesis testing, test statistic,%%
null hypothesis, alternative hypothesis, p-value,%%
type 1 error, type 2 error, power of a test
Questions on HW/Quiz, etc
bin size for histograms (Old Faithful eruption times)
Nothing new today: just going to put all the pieces together
Two inference tasks
estimating a paramter
1) get sample
2) compute statistic from sample
3) determine the quality of that statistic as an
estimate for paramter
a) confidence level
b) confidence interval, margin of error
testing a hypothesis
Video -- Against All Odds #23 (01:40 - 20:15)
Woburn Leukemia, BLS stats, example computations
Confidence Intervals for proportions
conditions under which the math applies
1) parameter must have a fixed (unknown value) for population
2) simple random sample or repeatable experiment
3) sample includes 5 of each outcome
4) population at least 10 times size of sample
the math:
distribution of sample proportions (statistic) will be
approximately normal N(p,root(p(1-p)/n)
example: suppose fair coin (50% heads)
flip it 100 times
flip it 400 times
flip it 1600 times
for each: ______% of time with _______
______% of time between _____ and _____
example: public opinion poll (suppose 30% rate)
sample size 1500
unknown p, what do we do?
note that (p)(1-p) < .25, so use .25
note that p-hat is usually very close to p, especially if
the sample is large
example: sample 1600 people and 500 people say yes
example: Reeses' pieces
Testing a hypothesis
1) determine null and alternative hypotheses
2) collect data
3) compute test statistic
test stat is a measure of how true the
null hypothesis seems to be
4) determine likelihood of such an extreme test
statistic if null hypothesis is true (p-value)
5) make a decision
Testing Hypothesis for Proportions
test statistic is z-score
example: predicting election outcomes
Hugo -- 13 times in 30 rolls; how unusual is that?
have students roll 30 dice several times and count number of
6's rolled (work in pairs)