Stat 301 – Day 14 Review

Previously Instead of sampling from a process  Each trick or treater makes a “random” choice of what item to select; Sarah randomly picks a solution we are treating the outcomes as fixed  (e.g., whether or not someone has hearing loss, whether word has letter e) and modelling the randomness in which sample we end up  Random sampling error Turns out we can usually model the randomness the same way  Independent observations

Last Time When we are sampling from a large population, we can still apply the binomial and/or normal distributions as an approximation  Population size does not matter! (Sampling distribution same center, spread, shape)  Large = at least 20 times the sample size  If not, should technically apply a “population correction factor” to the standard deviation (see Appendix)

Central Limit Theorem

Last Time

Finite Population… Can consider a continuity correction here as well!

Investigation % ci: (.17,.206) I’m 95% confident that 17% to 20.6% of all US teens have hearing loss. This is consistent with our test because 0.2 (hypothesized value of  ) is in this interval – plausible value for .

Exam 1 Each student has access to computer  Need 1-2 volunteers to bring laptop Open two pages of notes, applets, R, calculator  You are not to use any other aids  I can often answer questions on technology  Submit notes pages with exam Will set up dividers at beginning of exam Optional Q&A Session 6-7pm tonight

Study Advice Study like it is a closed book exam  Organize your notes but don’t expect much hunting and reading time  Work problems on a blank piece of paper See online solutions, Chapter 1 Examples Questions similar in format to HW questions  Careful interpretation in own words  Show details of calculations, technology use  Will not involve simple replication of previous exercises Apply what you have learned in new ways

What you have learned Making conclusions about process from sample: 1) How do we obtain a p-value comparing our sample statistic to a hypothesized parameter value? Ho/Ha Simulation/Binomial/Normal probability model (Binomial process, null) p-value/Test statistic (Continuity correction) Types of Error, Power 2) How do we estimate the population parameter based on the observed statistic? Plausible values/Confidence interval/Confidence level Simulation/Binomial/Normal probability model (Plus Four) Margin-of-error

What you have learned 3) Can we generalize from sample back to population or process? How do we select a good sample? Non-sampling errors

Types of problems Calculation problems  Assess evidence vs. estimate parameter  What do the simulations tell us?  Choice of method Evaluating results  Validity  Sample selection issues, inc. nonsampling errors  Generalizability Interpretations, properties, what if…?

Study Advice Review (complete) investigations, study conclusions Review graded HW, solutions Review practice problems, quizzes (concepts) Try review problems, check answers Try end of chapter examples, check answers See also technology guides, glossary Ask more questions, Review PolyLearn Q&A

Terminology cautions Percentage vs. proportion (vs. number of) Bias vs. precision (vs. representative, accurate) Number of samples vs. sample size Generalizability: To what larger population or process are you willing to apply these conclusions Confidence vs. significance Evaluate (decision) vs. Interpret (what measuring)

Test-taking Advice Exam worth approximately 50 points  Mixture of short-answer and more open ended answers, maybe even a couple of multiple choice Often do not have to answer questions (even subparts) in order Get something written down  Start with a sketch? Translate into symbols? Make sure it’s clear where your calculations came from  Which technology, inputs

Advice Practice drawing well-labeled sketches Words to avoid: It, Proof, Data Words to only use when you mean it: probability, confidence, significant, random Work out problems from scratch  Practice setting up (what is step 1?)

Example: Voter Turnout Statistic: 68.2% of random sample of 2613 eligible voters claimed to have voted in 1996 Parameter: FEC reports 49.0% actually voted What are some possible explanations for why these values differ?  Those in sample do not represent population  Those in sample were not honest  Statistics vary from sample to sample and may differ from parameter by chance Which of these explanations can we eliminate?

Example: Power A plastics manufacturer will change the warranty on his plastic trash cans if the data from 20 cans strongly suggests that fewer than 90% of such cans would survive the 6- year period. (a) How many cans would need to survive to convince you to reject the null hypothesis (b) What is the power against the alternative value of 80%?

Example: Power, cont. Null hypothesis: 90% survive Sample size: 20 What would convince you  <.90? Expect about 18 to survive P(X < 16) =.1330 P(X < 15) =.0432 P( <.75) =.0432

Example: Power (b) What is the power against the alternative value of 80%? How often do X < 15 when  =.80 If  =.80, I will correctly reject the null hypothesis that  =.90 in about 37% of samples Kinda small… not a very large sample size and not a very large difference

Practice problem 1.14 (p. 94) Representative vs. accuracy  Bias vs. precision Sample size vs. number of samples