Hypothesis testing is a statistical procedure used to determine if a hypothesis should be accepted or rejected based on sample data. It involves stating the null and alternative hypotheses, selecting a significance level, choosing a test statistic and distribution, determining decision rules based on critical values, collecting a sample, computing the test statistic, and comparing it to the critical value to either reject or fail to reject the null hypothesis. The power of a test measures how reliable its results are based on the probabilities of type 1 and type 2 errors. Limitations include uncertainty due to probability, misconceptions about the purpose of tests, samples not perfectly representing populations, and tests only indicating differences without explanation.

1. Dr.Sumitha Franklin
Assistant Professor, Department of Economics
St.Paul’s College,Kalamassery

2. WHAT IS HYPOTHESIS TESTING
 A PROCEDURE , BASED ON SAMPLING EVIDENCE
AND PROBABILITY THEORY , USED TO
DETERMINE WHETHER THE HYPOTHESIS IS A
REASONABLE STATEMENT AND SHOULD NOT BE
REJECTED , OR IS UNREASONABLE AND SHOULD
BE REJECTED.

3. BASIC COMPONENTS OF
HYPOTHESIS TESTING
 NULL HYPOTHESIS :- THE HYPOTHESIS TO BE
TESTED FOR ACCEPTANCE OR REJECTION
DENOTED BY H◦
 ALTERNATIVE HYPOTHESIS :- THE HYPOTHESIS
ACCEPTED WHEN THE NULL HYPOTHESIS IS
REJECTED USUALLY DENOTED BY HA
 USUALLY BOTH NULL AND ALTERNATIVE
HYPOTHESIS ARE STATEMENTS REGARDING
THE VALUE OF POPULATION PARAMETERS

4. CONTD…
 LEVEL OF SIGNIFICANCE :- SIGNIFICANCE LEVEL
IS THE MAXIMUM VALUE OF PROBABILITY OF
REJECTING H◦ WHEN IT HAPPENS TO BE TRUE
,ie, THE PROBABILITY OF TYPE 1 ERROR
DENOTED BY α
 DECISION RULE :- THE RULE BASED ON WHICH
THE NULL HYPOTHESIS IS EITHER REJECTED
OR ACCEPTED.

5. STEPS IN HYPOTHESIS TESTING
 STATE THE NULL HYPOTHESIS AND ALTERNATIVE
HYPOTHESIS
Ex. H◦: µ = 10 HA :µ≠10
 SELECTING A SIGNIFICANCE LEVEL
THE HYPOTHESIS IS TESTED ON A
PREDETERMINED LEVEL OF SIGNIFICANCE AND
AS SUCH THE SAME SHOULD BE SPECIFIED.
GENERALLY , IN PRACTICE , WE TAKE 5% OR 1% AS
THE SIGNIFICANCE LEVEL
0.10 FOR POLITICAL POLLING , 0.5 FOR MARKET RESEARCH PROJECTS , 0.01 FOR QUALITY
ASSURANCE WORK

6. CONTD…
 DECIDING THE DISTRIBUTION AND THE TEST
STATISTIC TO USE
BASED ON THE PARAMETER UPON WHICH THE
HYPOTHESES ARE SET UP ,SAMPLE SIZE AND THE
PARAMTERS KNOWN WE DECIDE ON THE TEST
SATATISTIC TO USE AND ASSUME A SAMPLING
DISTRIBUTION WHICH THE TEST STATISTIC IS
ASSUMED TO FOLLOW.
GENERALLY THE CHOICE REMAINS BETWEEN
NORMAL AND t DISTRIBUTION

7. CONTD…
 STATE THE DECISION RULES
THE RULE ACCORDING TO WHICH THE NULL
HYPOTHESIS IS REJECTED OR ACCEPTED ARE
SPECIFIED.
HERE THE CRITICAL VALUE OF THE TEST STATISTIC
IS DETERMINED ACCORDING TO THE
SIGNIFICANCE LEVEL. THE CRITICAL VALUE IS
THE VALUE OF TEST STATISTIC THAT DIVIDES
THE RANGE OF VALUES OF TEST STATISTIC INTO
REJECTION AND ACCEPTANCE REGIONS.

8. CONTD…
 SELECTING A RANDOM SAMPLE AND
COMPUTING THE TEST STATISTC BASED ON THE
SAMPLE VALUES
 COMPARE THE TEST STATISTIC WITH THE
CRITICAL VALUE
IF THE COMPUTED VALUE FALLS IN THE REJECTION
REGION, WE REJECT THE NULL HYPOTHESIS AND
OTHERWISE WE ACCEPT THE NULL HYPOTHESIS.

9. POWER OF A TEST
 IT IS A MEASURE OF HOW RELIABLE THE TEST
RESULTS ARE.
TYPE 1 ERROR HAS A PRE ASSIGNED PROBABILITY.
THE PROBABILITY OF ACCEPTING THE NULL
HYPOTHESIS WHEN IT IS FALSE IS KNOWN AS
THE PROBABILITY OF TYPE 2 ERROR AND IS
DENOTED BY ß
THEN POWER OF A TEST IS
Þ=1-ß
THE NEARER THE VALUE OF POWER TO 1 , THE
MORE RELIABLE IS THE TEST RESULTS.

10. LIMITATIONS OF THE TESTS
 UNCERTAINTY AS IT EMPLOYS PROBABILITY
 MISCONCEPTION OF TESTS BEING DECISION MAKING TOOLS RATHER THAN
AIDS TO DECISION MAKING
 SAMPLES MAY NOT ACTUALLY GIVE THE TRUE CHARACTERISTICS OF THE
POPULATION
 TESTS ONLY INDICATES THAT THERE IS DIFFERENCES OR NOT . IT DOESNOT
EXPLAIN WHY THERE IS DIFFERENCES , IF THERE IS
Thank you