Ten things about Inference AP Statistics, Second Semester Review

Population vs. Sample µ, mean σ, standard deviation p, proportion ρ, coefficient of correlation β, slope x-bar, mean s, standard deviation p-hat, proportion R, coefficient of correlation b, slope

Census vs. Sample What we want… What we can easily find out… To know what is going on at the population level What we can easily find out… What is going on at the sample level What we plan for… That representative sample will allow us to make statements about the population without actually doing a census

In General Sampling creates statistic which is an estimate to some unknown population parameter That statistic can be used to create an interval in which we think the population parameter exists Or That statistic can be used as evidence against some claim

Decisions, Decisions Z-Test T-Test 1-Prop Z-Test 2-Sample Z-Test 2-Sample T-Test 2-Prop Z-Test LinReg Test Chi-square GOF Test Chi-square Test Z-Interval T-Interval 1-Prop Z-Interval 2-Sample Z-Interval 2-Sample T-Interval 2-Prop Z-Interval

What do we mean by significant? When we say the test was significant at the α=.05 level, we mean… When we assume H0 is true these sample results (or more extreme) would happen by chance less than 5% of time

How do we interpret 95% confidence interval? “With 95% confidence, we believe the true parameter from the population of interest lies between these two values.” Replace the word parameter with the parameter used in context Replace the words population of interest with the context

What do we mean by 95% confident? That if we performed this sampling with the same sample size on the same population many, many times and calculated the confidence interval each time 95% of the confidence intervals would include the parameter that we were trying to estimate Probability