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Hypothesis Testing - Coggle Diagram

- - - - the research hypothesis is the conjecture or supposition that motivates the research
        
        research hypothesis lead directly to statistical hypothesis
    - - statistical hypothesis are hypotheses that are stated in such a way that they may be evaluated by appropriate statistical techniques
  - - - Null hypothesis is the hypothesis to be tasted
        
        H=0 ; Hypothesis of no difference
        
        rejected
        
        the data at hand are not compatible with the null hypothesis, but are supportive of some others hypothesis
        
        not rejected
        
        the data on which the test is based do not provide sufficient evidence to cause rejection
        
        alternative hypothesis
        
        statement of what we will believe is true if our sample data cause us to reject the null hypothesis
        
        research hypothesis = alternative hypothesis
      - Rules
        
        what you hope or expect to be able to conclude as a result of the test usually should be placed in the alternative hypothesis
        
        the null hypothesis should contain a statement of equality, either
        
        =>
        
        <=
        
        =
        
        the null hypothesis is the hypothesis that is tested
        
        the null and alternative hypotheis are complementary
    - - ex: the standard normal distribution if the null hypothesis is true and the assumptions are met
    - - non rejected region
        
        to not reject the null hypothesis if the computed value of the test statistics is one of the values in the next non rejections region
      - rejection region
        
        if the value if the test statistics that we compute from our sample is one of the values in the rejection region
      - Significance Level
        
        the level of significance alfa is a probability and in fact is the probability of rejecting a true null hypothesis
      - Type of error
        
        Type 1 error
        
        the error committed when a true null hypothesis is rejected
        
        Type 2 error
        
        the error committed when a false null hypothesis is not rejected
        
        Beta
- - - - Z test
    - - t-test
- - - - Z-test
    - - population variance equal
        
        t-test; sp^2
      - population variance unequal
        
        t' test