Stat 512 – Lecture 10 Cautions with Inference Open Applets page and Minitab and see me…

Last Time – Confidence Intervals Want to specify a range of plausible values for the parameter based on the sample result General form: Estimate of parameter + margin of error (lower endpoint, upper endpoint) Margin of error = critical value × SE(estimate)  Measures the expected size of the random sampling “error” (variability)

Last Time – Confidence Intervals Sample estimate determines the midpoint of the interval Sample size, standard error, confidence level determine the width of the interval

Example 5: What do we mean by “confidence”? Determine confidence interval using your sample proportion of orange candies… Did everyone obtain the same interval? Will everyone’s interval capture  ?

Interpretation of confidence What is the reliability of this procedure…  Assuming the Central Limit Theorem applies, how often will a C% confidence interval succeed in capturing the population parameter  To explore this, have to pretend we know the population parameter “Simulating Confidence Intervals” applet…

Interpretation of confidence What if I put all of these confidence intervals into a bag and randomly selected one? The confidence level is a probability statement about the method, not individual intervals  If we had millions of intervals…  Sample size?

Examples

Morals Garbage in  Garbage out! Inference is not necessary when you have conducted a census! Duality of confidence intervals and (two- sided) tests Statistical significance vs. practice significance  Strength of evidence vs. size of effect Confidence intervals vs. prediction intervals Type I and Type II Errors

For Tuesday Review!  Format of exam  What you need to know how to do (online)  Review problems from text (solutions in back)  Diagnostic questions (solutions online) Complete “PP 9.5” in Blackboard  Ask (at least) one question of the material  Submit a possible exam question