#--------------------------------------------------------- # File: MIT18_05S22_in-class23-script.txt # Author: Jeremy Orloff # # MIT OpenCourseWare: https://ocw.mit.edu # 18.05 Introduction to Probability and Statistics # Spring 2022 # For information about citing these materials or our Terms of Use, visit: # https://ocw.mit.edu/terms. # #--------------------------------------------------------- Class 23 Confidence intervals Jen Slide 1: Slide 2: Announcement/Agenda (2 minutes) Slide 3: R Quiz notes (4 minutes) Slide 4: Polling confidence interval: (2 minutes) conservative rule-of-thumb -(is a conservative CI) Slide 5: Binomial proportion. (2 minutes) Note: binomial proportion means the probability in the Bernoulli RV. That is, the proportion of heads/yeses/successes Slide 6: 1. BOARD question polling (work: 9 minutes, discuss 6 minutes) They should get these pretty well. For (c) they might give the exact or the rule-of-thumb 95% interval Go through the answers carefully to show how to organize them. It shouldn't require any derivations. E.g. (b) Margin of error = z_{0.1}/2\sqrt{n} = 0.01 z_{0.1} = qnorm(0.9) = 1.2816. So, 50*1.2816 = \sqrt{n} So, n = 4106 Slide 7: CLICKER QUESTION How many in the poll (5 minutes) Ans (1/.04)^2 = 625 I expect this will be easy, so can quickly walk through the computation Slide 8ab: Discussion question polling (6 minutes) What are some problems with overnight polling DISCUSSION: --Samples are not representative --Adjustments are easy to get wrong Slide 9: large sample confidence intervals (2 minutes) Brief description we do not have a question on it Key: CLT Slide 10: Review slide (2 min) From last time: No explanations. We are going to revisit these formulas in a few slides Jerry Slide 11: Three views (2 minutes) This is in the reading Slides 12, 13: standardized statistics (5 minutes) Go through the pivot for z DO NOT show them pivot for t and chi-square If time after next BQ can show it then Slide 14: View 2 hypothesis tests (5 minutes) Emphasize CI is a range of theta, rejection region is a range of x Illustrate this on a x-theta plane. Slide 15-17: BOARD question: Confidence intervals and non-rejection regions (work: 12 minutes, discussion 6 minutes) DISCUSSION Key: non-rejection regions horizontal: i.e. range of xbar confidence intervals vertical: i.e. range of mu Both run between same guides, so xbar in non-reject for mu <--> mu in CI for xbar Slide 18: Formal definition (3 minutes) Show and make one comment --it formalizes what we did in view 2. It's not essential that they know this.