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HYPOTHESIS TESTING, The original diagram, has pics in it, it can be found…

- - - - Mean:
        
        pop. distr. is normal => sampling distr. is normal
        
        n>30
        
        n not large, pop. distr. unknown => assume pop. distr is normal
      - Proportion
  - - - Testing for pop. mean
        
        σ known => use Z table
        
        σ unknown => use t table
      - Testing for pop. proportion
        
        Use Z table
  - - - σ known => find Critical value Z using α or α/2 depends on types of test
      - σ unknown => find Critical value t using α or α/2 depends on types of test , and degree of freedom (n-1)
      - Calculate test statistic
        
        Testing for mean σ known
        
        Testing for mean σ unknown
        
        Testing for proportion
      - Compare "Z" or "t" find in Step 6 with Critical Value in Step 5.
        
        Check whether it is in the Rejection Region or not.
        
        Make statistical decision
        => Reject Ho
        => Do not Reject Ho
    - - Calculate test statistics Z
        
        Testing for mean σ known
        
        Testing for proportion
      - Using test statistic find in step 5, calculate p-value
      - Compare p-value find in Step 6 with α
        
        Make statistical decision
        => p-value < α : Reject Ho
        => p-value > α : Do not reject Ho
  - - - As we reject Ho, with (1-α ) level of confidence, we can conclude that there is sufficient evidence that ..... (statement Ha in the context)
      - As we donot reject Ho, with (1-α) level of confidence, we can conclude that there is not sufficient evidence that ...... (statement Ha in the context)
  - - - Reject Ho: Making Type 1 Error: We conclude that there is sufficient evidence that (the statement Ha in the context) but in fact (statement Ho in the context)
      - Do not reject Ho: Making Type II Error: We conclude that there is not sufficient evidence that (statement Ha in the context) but in fact (statement Ha in the context)
- - - - Reject a true null hypothesis or Reject Ho when Ho is true
      - (1-α ) Confidence level
      - P(type I error) = α (level of significance)
    - - Failed to reject a false null hypothesis or Fail/Do not reject Ho when Ho is false
      - (1-β ): Power of the test
      - P(type II error) = β
  - - - increase (1-α)
    - - α increase => β decrease
        σ increase => β decrease
        n increase => σ decrease => β decrease
- - - - When sign of Ha is "<"
    - - When sign of Ha is ">"