# STAB22H3 Lecture Notes - Confidence Interval, Unimodality, True Value

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

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

- 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

## Document Summary

When have to make decision based on data, use hypo test. For mean of qvar main text, p617. What - time it takes to get to school. 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. Qdata typically reports numerical val. for each subj. Regardless of what popn the random sample is retrieved from, shpape of sampling distrib approx. Larger the n more closely that normal approximates sampling distrib of mean. This formula req. that we know true popn sd (sigma) p619. 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.