Department

Economics for Management StudiesCourse Code

MGEB12H3Professor

Victor YuStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**8 pages of the document.**Department of Management, UTSC

MGEB12 Quantitative Methods in Economics II - Lecture 02

Chapter 9 - Hypothesis Testing of Mean, Population Variance Unknown

1. Introduction

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2. t-Distributed Random Variable

â€¢t-distribution is symmetric just like normal distribution.

â€¢Degrees of freedom (d.f.) is # of independent pieces of information that goes into computing the standard

deviation s.

Expected value = E[t] = 0 Variance =

1

][

âˆ’

=

n

n

tVAR

where n = d.f.

â€¢The larger the degrees of freedom, the closer t-distribution resembles the standard normal distribution Z.

â€¢When d.f. n = 1000 it becomes practically standard normal Z.

â€¢Can use Table in Appendix B to lookup values of t-distribution.

oNormal distribution table Z gives lower (left) tail i.e. p[Z â‰¤ z]

ot-distribution table gives the upper (right) tail i.e., or p[tn-1 â‰¥ t]

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â€¢Table in Appendix B only provides a limited number of values, may need to use Linear Interpolation to

find additional values.

Given 2 points (x0,y0) and (x1,y1) to find value of y for x0 â‰¤ x â‰¤ x1:

)(

))((

01

010

0

xx

yyxx

yy

âˆ’

âˆ’âˆ’

+=

Given 2 points (x0,y0) and (x1,y1) to find value of x for y0 â‰¤ y â‰¤ y1:

)(

))((

01

010

0

yy

xxyy

xx

âˆ’

âˆ’âˆ’

+=

Example 1

X is t-distributed with d.f. = 9.

P[ X â‰¥ 1.833] =

P[x â‰¤ 3.25] =

P[X â‰¥ 4] =

P[X â‰¥ .6] =

P[ X â‰¥ 2] =

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