Section 7.1 Objectives
       • A practical introduction to hypothesis tests
       • How to state a null hypothesis and an alternative 
           hypothesis
       • How to Identify type I and type II errors and interpret 
           the level of significance
       • How to know whether to use a one-tailed or two-
           tailed statistical test and find a P-value
       • How to make and interpret a decision based on the 
           results of a statistical test
       • How to write a claim for a hypothesis test 
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                            Hypothesis Tests
       Hypothesis test 
       • A  process that uses sample statistics to test a claim 
           about the value of a population parameter.  
       • For example:  Consider a manufacturer that 
           advertises its new hybrid car has a mean gas mileage 
           of 50 miles per gallon. If you suspect that the mean 
           mileage is not 50 miles per gallon, how could you 
           show that the advertisement is false?
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                            Hypothesis Tests
       Statistical hypothesis 
       • A statement about a population parameter.
       • Carefully state a pair of hypotheses
            •  one that represents the claim 
            •  the other, its complement  
       • When one of these hypotheses is false, the other must 
           be true.
       • Either hypothesis—the null hypothesis or the 
           alternative hypothesis—may represent the original 
           claim.
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                       Stating a Hypothesis
       1. A null hypothesis H0 is a statistical hypothesis that 
              contains a statement of equality, such as , =, or .
       2. The alternative hypothesis H  is the complement of 
                                                                   a
              the null hypothesis. It is a statement that must be 
              true if H  is false and it contains a statement of strict 
                            0
              inequality, such as >,  , or <.
       The symbol H  is read as “H sub-zero” or “H naught” 
                                0
       and H  is read as “H sub-a.”
                  a
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                       Stating a Hypothesis
       • To write the null and alternative hypotheses, translate 
           the claim made about the population parameter from 
           a verbal statement to a mathematical statement.
       • Then, write its complement.
              H: μ ≤ k                        H: μ ≥ k                         H: μ = k
                 0                                0                               0
              H: μ > k                        H: μ < k                         H: μ ≠ k
                 a                                a                               a
       • Regardless of which pair of hypotheses you use, you 
           always assume μ = k and examine the sampling 
           distribution on the basis of this assumption.
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