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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.