Steps involved in hypothesis testing of the mean , Operation Research

 Statement of Hypothesis

The  two hypothesis  i  ,e,  null hypothesis  (H0) and Alternative Hypothesis (H1) are so  constructed  that if  one is  correct the other  is wrong. Generally the Null  Hypothesis  for  testing  the mean  will take  any one  of the followings  forms:

H0 : µ ≤ µ0         H0 : µ µ0                             H0 : µ = µ0

Where= population mean and  µ0  hypothesis value .  

Step 2. Specification  of Significant level

The validity  of H0 against H1 is then  ascertained  at a certain level of  significance. The  significance level stands  for the  confidence  with  which  the experimenter  rejects  or retains the null  hypothesis. Significance  level is usually  expressed as percentage or by the value  of α i ,e, 5% or α= =0.05.

Step3.  Formulation  of the Rejection and Acceptance Regions

The  followings  table give the typical  cases of  setting  up the  regions  of rejection acceptance for the various  cases of H0 with the  hypothesized  value   of the population mean.

Making  the Inference

On the  basis  of the  sample  mean  calculated from  the sample data a decision is made  from the  rule  given  in step4. If the samples  mean lies in the region of rejection, null hypothesis  H0 is rejected while  alternative HypothesisH1 is accepted. If  the samples  mean  lies in the region of acceptance the alternative  step has been  done. From  the  figure  above  one can  observe that the  area in the tails equal the  level of significance. For  one tailed test  appear in one tail  and for  two tailed test α/ 2 appears in  each  tail  of the  curve.

 

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