STATISTICS FOR BUSINESS
                           (Hypothesis testing for a single population)
                                                                                                 A nuclear power plant
                                                                                                adjacent to a residential area
     An hypothesis is giving an opinion or making a decision without objective information 
     Consider: Government announces
     "Radiation levels around a nuclear power plant are well below levels  considered harmful". 
     Two local  residents die of leukemia
     Does this  event make us conclude that the government is giving wrong information?
    It is wrong to accept,  or reject, a hypothesis about  a population parameter simply  by intuition. 
    One needs to  decide objectively on the  basis of measured sample information.
   Derek L WALLER ©                                                                                        2
                                       STATISTICS FOR BUSINESS
                            (Hypothesis testing for a single population)
                                                                                                    A nuclear power plant
                                                                                                  adjacent to a residential area
           Procedure for hypothesis testing 
      •   Select a random sample
      •   Measure the appropriate statistic - the mean or proportion
      •   Decide on the desired level of significance: (Say 5%)
      •   Determine if the statistic falls within an appropriate region of 
        acceptance
      •   Accept the hypothesis if the statistic falls into the acceptance region. 
           •
            Otherwise, reject it
      Even if a sample  statistic does fall in the area of acceptance, it does not prove 
      that the  null hypothesis, Ho, is true. There is  simply no statistical evidence to 
      reject it., 
   Derek L WALLER ©                                                                                           3
                                     STATISTICS FOR BUSINESS
                           (Hypothesis testing for a single population)
                                                                                               A nuclear power plant
                                                                                             adjacent to a residential area
         Nomenclature in hypothesis testing 
     Hypothesis:
     •  In a certain country, average age of population is 35 within a given significance 
        level
     •  Written as: H :µ  = 35
                      o  x
     •  Null hypothesis is that population mean is equal to 35
     Alternative hypothesis:
     •  Population mean is not equal to 35.
     •  That is the mean or average age is significantly different from 
        35
     •  Written as: H :µ   35
                      1  x
    Whenever the null hypothesis is rejected, accepted conclusion is the alternative hypothesis
    •   Binomial either “accept” or “reject”
   Derek L WALLER ©                                                                                     4
                                        STATISTICS FOR BUSINESS
                             (Hypothesis testing for a single population)
                                                                                                       A nuclear power plant
                                                                                                      adjacent to a residential area
     Concept of significance
      Exam grades - Case 1
     •   John has an A in the course on Business Statistic: Susan has an A
     •   Is the difference significant? NO
     Exam grades - Case 2
     •   Sarah has an A in the course on Business Statistics: Derek has a  C-
     •   Is the difference significant? YES
     Ages - Case 1
     •   Joan, Susan, and Mike are in the same class at university.
     •   Is there a significance difference in their age? PROBABLY NOT
     Ages- Case 2
     •   Angela is the granddaughter of  Kenneth
     •   Is there a significant difference in their ages? YES
      Automobile prices - Case 1
      •   Erin has just bought a new red Austin Mini automobile. Peter has just bought the same model, but green.
      •   Is there a significance difference in their purchase price? PROBABLY NOT
      Automobile prices - Case 2
      •   Pauline has just bought a new Austin Mini automobile. Jeffrey has just bought a Porsche.
      •   Is there a significant difference in their purchase price? YES
    Derek L WALLER ©                                                                                              5
                                        STATISTICS FOR BUSINESS
                             (Hypothesis testing for a single population)
                                                                                                      A nuclear power plant
                                                                                                     adjacent to a residential area
     Two-tailed hypothesis test
     Question asked: "Is there evidence of a difference?"
     Null hypothesis: Average age of a certain group is 35 years: Ho:µx = 35
     Alternative: Is there evidence that average age the group is different than 35 years: H :µ  ≠ 35
                                                                                             1  x
     At 10% significance, there is 5% in each tail
     If sample means falls within the non shaded area,
     accept the null hypothesis
      Reject the null hypothesis if
      sample mean falls in either of the shaded regions
   Derek L WALLER ©                                                                                              6