Class Notes (1,100,000)

CA (650,000)

UTSC (30,000)

Statistics (400)

STAB22H3 (200)

Ken Butler (30)

Lecture

This

**preview**shows pages 1-3. to view the full**23 pages of the document.**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

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

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

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

- 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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