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)