Hypothesis Testing and procedure

Hypothesis testing is based on hypothesis;


•“Hypothesis” is an assumption about an unknown population parameter;


•Hypothesis testing is a well defined procedure which helps in deciding objectively whether to accept or reject the hypothesis based on the information available from the sample;

Hypothesis Testing Procedure

STEP 1: SET NULL & ALTERNATIVE HYPOTHESIS:

•The assumption which we want to test is called the NULL hypothesis;


•It is symbolized as Ho;


•Null hypothesis is set with no difference (i.e. status quo) & considered true, unless and until it is proved by the collected sample data;


•Example, Ho :μ =500

“the null hypothesis is that the population mean is equal to 500”

The Alternative hypothesis, generally referred by H₁ or Ha is the logical opposite of the null hypothesis;

• H1 :μ ≠500;

• In other words, when null hypothesis is found to be true, the alternative hypothesis must be false; or vice versa;

• Rejection in null hypothesis indicates that the difference have statistical significance & acceptance in null hypothesis indicates that the difference are due to chance;

STEP2: SET UP A SUITABLE SIGNIFICANCE

•The level of significance, generally denoted by ‘α’ is the probability, which is attached to a null hypothesis, which may be rejected even when it is true;

•The level of significance is also known as the size of rejection region or size of critical region;

•It is generally specified before any samples are drawn, so that results obtained will not influence the direction to be taken;

•Any level of significance can be adopted in practice we either take 5% or 1% level of significance;

When we take 5% level of significance then there are about 5 chances out of 100 that we would reject the null hypothesis when it should be accepted i.e. we are about 95% confident that we have made the right decision;

•When the null hypothesis is rejected at α=0.5, test result is said to be significant;

•When the null hypothesis is rejected at α=0.01, test result is said to be highly significant;

STEP3: DETERMINATION OF A SUITABLE TEST STATISTIC

•Many of the test statistic that we shall encounter will have the following form:

STEP4 : SET THE DECISION RULE

•The next step for the researcher is to establish a critical region

•Acceptance region : when null hypothesis is accepted;

•Rejection region ; when null hypothesis is rejected;

STEP 5: COLLECT THE SAMPLE DATA


•Data is now collected;

•Appropriate sample statistic are computed;

STEP 6: ANALYSE THE DATA

•This involves selection of an appropriate probability distribution for a particular test;

•For example, when the sample is small (n<30) the use of normal probability distribution (Z) is not an accurate choice, (t) distribution needs to be used in this case;

•Some commonly used testing procedures are
Z, t, F & Chi square

STEP 7: ARRIVE AT A STATISTICAL CONCLUSION & BUSINESS IMPLICATION

•Statistical conclusion is a decision to accept or reject a null hypothesis;

•This depends on whether the computed test statistic falls in acceptance region or rejection region;


this video explains hypothesis testing and procedure