hypothesis testing chandru

7/29/2019 Hypothesis Testing Chandru

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HYPOTHESIS TESTINGHYPOTHESIS TESTINGHYPOTHESIS TESTINGHYPOTHESIS TESTING

Presented by:

CHANDRA SHEKAR B.M.

Research Scholar

Dept. of commerce,

Bangalore University.

Under the Guidance of

DR. K. NIRMALA

Faculty,

Dept. of commerce,

Bangalore University.

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• Meaning of Hypothesis

• Hypothesis Testing

• Related Terminologies

• Type I vs. Type II Error

CONTENTS

• αααα Level of Significance• Acceptance Region and Rejection Region

• Critical Value



WHAT’S AN HYPOTHESIS

• HYPOTHESIS

• An educated guess or the best answer to a

question, based on the most reliable factsavailable; a guess that will be TESTED

• In statistics, it is a claim or statementabout a property of a population

• It is a proposition the validity of which needs tobe tested



WHAT’S THIS ALL ABOUT?

• HYPOTHESIS TESTING

•• It is a standard procedure for testing a claim aboutIt is a standard procedure for testing a claim abouta property of a populationa property of a population



• STEPS IN HYPOTHESIS TESTING

1.1. GivenGiven aa Proposition,Proposition, statestate thethe NullNull HypothesisHypothesis andand

Alternate Alternate (Research)(Research) hypothesishypothesis inin operationaloperational termsterms

2.2. SelectSelect thethe Appropriate Appropriate statisticalstatistical testtest

3.3. SelectSelect thethe desireddesired levellevel of of significancesignificance

4.4. ComputeCompute thethe appropriateappropriate statisticstatistic fromfrom thethe samplesample datadata

5.5. StateState thethe conclusionconclusion of of aa hypothesishypothesis testtest inin simple,simple, nonnon--technicaltechnical termsterms..



NULL HYPOTHESIS VS. ALTERNATIVE HYPOTHESIS

NULL HYPOTHESIS

• Statement about the valueof a population parameter

ALTERNATIVE HYPOTHESIS

• Statement about the value of apopulation parameter that must betrue if the null hypothesis is false

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• Represented by H0

• Always stated as an

Equality

• Represented by H1

• Stated in on of three forms

• >

• <

• ≠≠≠≠



STEPSTEP 11:: GivenGiven aa Proposition,Proposition, statestate thethe NullNull HypothesisHypothesis andand Alternate Alternate(Research)(Research) hypothesishypothesis inin operationaloperational termsterms

PROPOSITIONPROPOSITION :: ChangesChanges inin production production process process will will resultresult inin betterbetter

product product (( IncreaseIncrease lifelife of of TyresTyres))GivenGiven:: MeanMean lifelife of of oldold TyresTyres == 4040,,000000kmkm

MeanMean lifelife of of New New TyresTyres == 4141,,200200kmkm

NULLNULL HYPOTHESISHYPOTHESISHH00 == ChangeChange inin production production process process will will notnot changechange lifelife of of TYRESTYRES

ALTERNATE ALTERNATE HYPOTHESISHYPOTHESIS

HH11 == ChangeChange inin production production process process will will changechange (improve)(improve) lifelife of of TYRESTYRES

HH00 : µ = 40,000 km: µ = 40,000 km

HH11 : µ > 40,000 km: µ > 40,000 km



STEPSTEP 22 :: SELECTSELECT THETHE APPROPRIATE APPROPRIATE STATISTICALSTATISTICAL TESTTEST

PARAMETRIC TESTS & NON PARAMETRIC TEST

(Assumes Parameters such as

mean, SD etc)

Z-TEST

(Do not assumes Parameters )

CHI-SQUARE TEST

T – TEST

F-TEST

ANOVA etc

MC NEMAR TEST

RANK SUM TEST etc



STEPSTEP 33 :: SELECTSELECT THETHE DESIREDDESIRED LEVELLEVEL OFOF SIGNIFICANCESIGNIFICANCE

Denoted byDenoted by αα

TheThe probability probability thatthat thethe testtest statisticstatistic will will fallfall inin thethe

criticalcritical regionregion when when thethe nullnull hypothesishypothesis isis actuallyactually

truetrue..

CCommon choices are 0.05, 0.01 and 0.10ommon choices are 0.05, 0.01 and 0.10



The The testtest statisticstatistic isis aa value value computedcomputed fromfrom thethe samplesampledata,data, andand itit isis usedused inin making making thethe decisiondecision aboutabout thethe

rejectionrejection of of thethe nullnull hypothesishypothesis..

STEP 4STEP 4 :: COMPUTE THE APPROPRIATE STATISTICCOMPUTE THE APPROPRIATE STATISTICFROM THE SAMPLE DATA FROM THE SAMPLE DATA

z =

x - µ x

σ

n

Test statisticTest statistic

for meanfor mean zcal

= 3.2



STEP 5STEP 5 :: DECISION &DECISION & STATE THE CONCLUSION OFSTATE THE CONCLUSION OFHYPOTHESIS TEST IN SIMPLE, NONHYPOTHESIS TEST IN SIMPLE, NON--TECHNICAL TERMS.TECHNICAL TERMS.

αα = 0.05= 0.05

Acceptance Region Reject H0

zCal = 3.2

µ

z (Table value) = ± 1.64

0 1.64 3.2



As seen above the computed value of z=3.2 falls in the

rejection region.

Thus we reject the null hypothesis that u=40,0000 kmsand alternate hypothesis is accepted

DECISIONDECISION

ALTERNATE ALTERNATE HYPOTHESISHYPOTHESIS

HH11 == CHANGECHANGE ININ PRODUCTIONPRODUCTION PROCESSPROCESS WILLWILLCHANGECHANGE (IMPROVE)(IMPROVE) LIFELIFE OFOF TYRESTYRES

HH11 : µ > 40,000 km: µ > 40,000 km



REJECTION REGION / CRITICALREJECTION REGION / CRITICALREGIONREGION

Set of all values of the test statistic that would cause aSet of all values of the test statistic that would cause arejection of the null hypothesisrejection of the null hypothesis

CriticalRegions

5%5%



CRITICAL VALUECRITICAL VALUE

Fail to re ect H Re ect H

Any value that separates the critical region (where we reject Any value that separates the critical region (where we rejectthe null hypothesis) from the values of the test statisticthe null hypothesis) from the values of the test statistic

that do not lead to a rejection of the null hypothesisthat do not lead to a rejection of the null hypothesis

Critical Value( z score )



PP--VALUE VALUE

TheThe P P --value value (or(or p p --value or probability value) is the probability value or probability value) is the probability

of getting a value of the test statistic that isof getting a value of the test statistic that is at least at least as extreme as extreme

null hypothesis is true. The null hypothesis is rejected if thenull hypothesis is true. The null hypothesis is rejected if the

P P --value is very small, such as 0.05 or less. value is very small, such as 0.05 or less.



TwoTwo--tailed Testtailed Test

H H 00:: ==

H H 11:: ≠≠≠≠≠≠≠≠

αα is divided equallyis divided equally between thebetween thetwo tails of the criticaltwo tails of the critical regionregion

Means less than or greater thanMeans less than or greater than

Values that differ significantly from HValues that differ significantly from H00



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hypothesis testing chandru

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