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# 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.
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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.