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CONTENTS

Chapter 1. Hypothesis testing ..71.1. Introduction...7

1.12.Concepts of hypothesis testing ...7

1.13. The null and alternative hypothesis 8

1.14. Tails of the test...11

Eercises..14

1.2. Tests of the !ean of a nor!al distri"ution# $opulation variance

%no&n ....1'

1.3. Tests of the !ean of a nor!al distri"ution# $opulation variance

un%no&n ()arge sa!ple si*e+..18

Eercises..211.4. ,ypothesis testing using thep-value approaches ..23

Eercises..2'

1.'. Tests of the !ean of a nor!al distri"ution# $opulation variance

un%no&n. !all sa!ples .2/

Eercises 20

1./. Tests of the population proportion ()arge sa!ple+ . 32

Eercises...34

1.7. Tests of the variance of a nor!al distri"ution 3/Eercises 38

1.8. Tests for the difference "et&een t&o population !eans ..4

1.8.1. Tests "ased on paired sa!ples4

Eercises...43

1.8.2. Tests "ased on independent sa!ples (no&n variance

or large sa!ple si*e+ 44

Eercises ..47

1.8.3. Tests "ased on independent sa!ples ($opulation variances

are un%no&n and eual+...40

Eercises'2

1.0. Tests for the difference "et&een t&o population proportions

()arge sa!ples+ .''

Eercises.'0

Chapter 2. Some nonparametric tests......./12.1. Introduction./1

2.2.1. The ign test for paired or !atched sa!ples. ./2

2.2.2. The sign test# or!al approi!ation ()arge sa!ples+ .. /'

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Eercises/7

2.3. The 5ilcoon signed test ..7

2.3.1. The 5ilcoon signed test for paired sa!ples

(s!all sa!ple si*e+....7

2.3.2. The 5ilcoon signed test for paired sa!ples(large sa!ple si*e+....72

Eercises74

2.4. The 6ann5hitney test..77

Eercises82

Chapter 3. Simple linear regression.....843.1. Introduction 84

3.2. The scatter diagra!.....84

3.3. Correlation analysis.8/3.3.1. ,ypothesis test for correlation .80

Eercises 01

3.4. pear!an ran% correlation ......03

Eercises 0'

3.'. The linear regression !odel 0/

3.'. 1. )east suares coefficient esti!ators . 08

3.'.2. )east suare procedure ... .00

3.'.3. Interpretation of a and b......123.'.4. ssu!ptions of the regression !odel .13

Eercises.14

3./. The eplanatory po&er of a linear regression euation .1/

3./.1. Coefficient of deter!ination 2R .....10

3./.2. Esti!ation of !odel error variance 11

Eercises 111

3.7. tatistical inference# ,ypothesis tests and confidence

intervals.1133.7.1. ,ypothesis testing a"out ....114

3.7.2. Confidence intervals for the population regression slope ..11/

Eercises.117

3.8. 9sing the regression !odel for prediction a particular

value ofy12

Eercises .123

Chapter 4. Multiple regression analysis.12'4.1. Introduction.12'

4.2. 6ultiple regression !odel 12'

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4.3. tandard assu!ptions for the !ultiple regression !odels ..127

4.4. The eplanatory po&er of a !ultiple regression euation..127

4.4.1. Esti!ation of error variance distri"ution.127

4.4.2. The coefficient of deter!ination..128

4.4.3. d:usted coefficient of deter!ination..1204.4.4. $redictions fro! the !ultiple regression !odels.13

Eercises.13

4.'. Co!puter solution of !ultiple regressions .132

4./. Confidence interval for individual coefficients ..138

Eercises.130

4.7. Test of hypothesis a"out individual coefficients .143

4.8. Tests on sets of regression para!eters.14'

Eercises. 14/4.0. ;u!!y varia"les in the regression !odels.1'

Eercises.1''

Chapter 5. nalysis o! "ariance #NO$% ..1'0'.1. Introduction.....1'0

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7.1.2. 9n&eighted aggregate price inde....23

7.1.3. &eighted aggregate price inde 2'

7.1.4. &eighted aggregate uantity inde2/

7.2. Co!!only used inde nu!"ers...2/

7.3. ;eflating a series "y price indees...27Eercises..20

7.4 nonpara!etric test for rando!ness211

7.4.1. The runs test for the s!all sa!ple si*es211

7.4.2. The run test for the large sa!ple si*es..212

Eercises.213

7.'. Co!ponents of ti!e series...21/

7./. 6oving averages..217

Eercises.227.7. Eponential s!oothing221

Eercises.224

7.8. ;ou"le eponential s!oothing (,olt5inters eponential

forecasting !odel+...22/

Eercises.23

ppendi ....232

>eferences.. 2'3

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