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Lecture

STAB22H3 Lecture Notes - Confidence Interval, Unimodality, True Value


Department
Statistics
Course Code
STAB22H3
Professor
Ken Butler

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inferences about means (chapter 23)
STUDENT'S T
-> ASSUMPTIONS & CONDITIONS
1. INDEPENDENCE ASSUMPTION
- randomization condition
- 10%
2. NORMALITY
- nearly normal condition
- when have to make decision based on data, use hypo test
-----------------------------------------
WHERE ARE WE GOING?
- CHP23:
1. making CI
2. testing hypothesises
... for mean of qvar
main text, p617
[1]
WHO - 2ndry school students
WHAT - Time it takes to get to school
UNITS - min.
WHEN - 2007-2008
WHERE - Ontario

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WHY - Pt of CensusAtSchool Project
- want to get a feel as to what is avg time it takes for all Ontario students to get to
school
- n = 40 Ontario 2ndry school students, SRS
HOW DOES DATA REGARDING MEANS DIFFER FROM PROPORTIONS
- *impt way: prop's typically reported as summaries
- individual response is either: "succcess"/"failure"
- qdata typically reports numerical val. for each subj.
- summarized w/ means & SD's
GETTING STARTED
[1]
CLT SUMMARY

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- regardless of what popn the random sample is retrieved from, shpape of sampling
distrib approx. Normal, given
n
sufficently largr
- larger the
n
more closely that Normal approximates sampling distrib of mean
- this formula req. that we know true popn SD (sigma)
p619
CLT Problem
- req. that to model smapling distrib. of mean from random sample of qdata, need true
popn SD
- for means, knowing about sample mean does not tell us ath about standard deviation
of mean
- know
n
, but sigma couild be ath
- resol'n: est. popn parameter sigma with
s
= sample SD (based on data)
GREEN BOX:
- b/c SD of sampling distrib model is being estimated from data, SD called SE (standard
error)
- SE = estimated SD of samplign distrib model for means
main text (con.; p619)
STANDARD ERROR WITH NORMAL MODEL
- this worked for larger sample sizes
- prob's w/ smaller samples
- too much variance in data to fit with Normal model properly
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