3 Types of Hypothesis Test Using the t Statistic

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					            3 Types of Hypothesis Test Using the t Statistic (t Tests)

    1) The 1-sample t-Test
          Similar set-up to z-Test we have already done (but uses t instead of z); hypothesis is
          about the value of a population mean (µ).
          Example: A diet self-help book estimates that the average 1 ounce chocolate chip
          cookie contains 110 calories. A nutritionist suspects this estimate is low. She
          randomly samples 15 different brands of 1-ounce chocolate chip cookies. The calorie
          counts are shown below. Is there evidence at α = .05 that the average calorie content
          is greater than 110 calories per cookie?
          100 125 150 160 185 125 90 145 160 100 150 120 85 105 110

    2) The matched pairs t-Test (a.k.a. 2 dependent samples)
          In these scenarios, two sets of data are collected, but each value in the first data set is
          linked in some way to a value in the other data set. Hypothesis is about the average
          difference between the two values (µdif).
          Examples:
  a) Is there evidence that on      b) Is there evidence that on        c) Is there evidence that on
     average, wives spend              average, a certain drug              average, more men in
     more time per week on             lowers cholesterol?                  city X receive speeding
     household chores than                                                  tickets each year than do
                                  Sample Data (cholesterol
     their husbands spend?                                                  women?
                                  level– initial and after 6 weeks
Sample Data (hours/wk):           of taking drug):                   Sample Data (number of
                                                                     tickets received by each
 Couple     Wife      Husband       Patient    Before     After      gender for given year):
   1         9.4          3.6          1        270        240
                                                                        Year       Men      Women
   2        12.5        15.1           2        230        235
                                                                        2008      28,471 29,002
   …               (etc.)             …             (etc.)
                                                                        2007      24,216 24,105
                                                                          …             (etc.)
(Link: matched pairs are from     (Link: matched pairs are from
same couple)                      same patient)
                                                                     (Link: matched pairs are from
                                                                     same year)

   3) The 2-sample t-test (a.k.a. 2 independent samples)
            In this scenario, the goal is to compare the means of two different populations.
            Therefore, there is a sample from each population, and values from one sample are
            not linked in any way to the values from the other sample. Hypothesis is about how
            the two means compare to each other (µ1 and µ2)
            Examples:
a) Is there evidence that on average, movie        b) Is there evidence that on average, pro
   ticket prices are higher in Atlanta than they        football players have shorter careers than
   are in Dawsonville?                                  pro baseball players?
   Sample Data:                                        Sample Data (years in sport before retiring)
            Atlanta        Dawsonville                    Football players Baseball players
             $8.75             $8.00                               8                 12
             $9.50             $6.75                              11                  4
             $7.50              etc.                             etc.                 9
              etc.                                                                  etc.