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					Essentials of Marketing
       Research
       Kumar, Aaker Day
 Instructor‟s Presentation Slides
  Essentials of Marketing Research   Kumar, Aaker, Day
          Chapter Sixteen
    Hypothesis Testing:
   Means and Proportions

Essentials of Marketing Research   Kumar, Aaker, Day
       Hypothesis Testing For
     Differences Between Means
   Commonly used in experimental research
   Statistical technique used is analysis Of variance
         (ANOVA)
    Hypothesis Testing Criteria Depends on
   Whether the samples are obtained from different
    or related populations
   Whether the population is known on not known
   If the population standard deviation is not known,
    whether they can be assumed to be equal or not
          Essentials of Marketing Research   Kumar, Aaker, Day
    The Probability Values (P-value)
    Approach to Hypothesis Testing
 P-value  provides researcher with alternative
  method of testing hypothesis without pre-
  specifying 
 Largest level of significance at which we
  would not reject ho
  Difference Between Using  and p-value
 Hypothesis        testing with a pre-specified 
      Researcheris trying to determine, "is the probability
      of what has been observed less than ?"
      Reject    or fail to reject ho accordingly
       Essentials of Marketing Research    Kumar, Aaker, Day
   The Probability Values (P-value)
Approach to Hypothesis Testing (Contd.)
    Using the p-Value
   Researcher can determine "how unlikely is the
    result that has been observed?"
   Decide whether to reject or fail to reject ho without
    being bound by a pre-specified significance level
   In general, the smaller the p-value, the greater is
    the researcher's confidence in sample findings
   P-value is generally sensitive to sample size
        A   large sample should yield a low p-value
   P-value can report the impact of the sample size
    on the reliability of the results
          Essentials of Marketing Research   Kumar, Aaker, Day
     Hypothesis Testing About
   a Single Mean - Step-by-Step
1) Formulate Hypotheses
2) Select appropriate formula
3) Select significance level
4) Calculate z or t statistic
5) Calculate degrees of freedom (for t-test)
6) Obtain critical value from table
7) Make decision regarding the Null-hypothesis



        Essentials of Marketing Research   Kumar, Aaker, Day
     Hypothesis Testing About
     a Single Mean - Example 1

 Ho:  = 5000 (hypothesized value of population)
 Ha:   5000 (alternative hypothesis)
 n = 100
 X = 4960
  = 250
  = 0.05


Rejection rule: if |zcalc| > z/2 then reject Ho.

         Essentials of Marketing Research   Kumar, Aaker, Day
      Hypothesis Testing About
      a Single Mean - Example 2
 Ho:  = 1000 (hypothesized value of population)
 Ha:   1000 (alternative hypothesis)
 n = 12
 X = 1087.1
 s = 191.6
  = 0.01


Rejection rule: if |tcalc| > tdf, /2 then reject Ho.

          Essentials of Marketing Research   Kumar, Aaker, Day
      Hypothesis Testing About
      a Single Mean - Example 3
 Ho:   1000 (hypothesized value of population)
 Ha:  > 1000 (alternative hypothesis)
 n = 12
 X = 1087.1
 s = 191.6
  = 0.05


Rejection rule: if tcalc > tdf,  then reject Ho.


          Essentials of Marketing Research   Kumar, Aaker, Day
        Confidence Intervals
 Hypothesis testing and Confidence Intervals
 are two sides of the same coin.



    ( X  )
 t                                 X  ts x  interval
       sx                                           estimate of 



      Essentials of Marketing Research       Kumar, Aaker, Day
               Confidence Interval Estimation

If  = .95 then,


Problem:
                                                  n = 75                 = .01

Since CI is for both sides, z-value is got for /2 = .005
Z /2 = 2.58




Test the hypothesis that the true mean weight of the Hawkeyes football
  team is greater than or equal to 300 pounds with  = .05
               Essentials of Marketing Research            Kumar, Aaker, Day
         H0:      uW  300
         H1:      uW < 300




At  = 0.05, CVZ = -1.645            (for a one-tailed test)
   Since Zts falls in the critical region

We ______________________ the null hypothesis




                Essentials of Marketing Research     Kumar, Aaker, Day
   Test the hypothesis that the true mean weight of the Hawkeyes
    football team is equal to 286 pounds with  = 0.01

                 H0:          uW = 286
                              uW  286




AT  = .01

    CVZ = 2.58

Since Zts < CvZ we __________________ the null hypothesis


              Essentials of Marketing Research   Kumar, Aaker, Day
Chain                        N                  Proportion of Stores
                                                Open for 24 hours
A                            40                 -45
B                            75                 -40

    H0:     PA = P B
    HA:     PA not equal to PB




          Essentials of Marketing Research   Kumar, Aaker, Day
And                                                          df = n1+n2-2
                                                             (n1-1) + (n2-1)
                                                             = .05
                                                             df = 113

      = weighted average of sample proportions



  Computation of tts would proceed as follows:




             Essentials of Marketing Research    Kumar, Aaker, Day
Since




then




and




                               -1.96                           +1.96
                      .025                                             .025
                          -                                            +
        Essentials of Marketing Research   Kumar, Aaker, Day
Descriptive Statistics for two samples of students, liberal arts majors (n = 317)
  and engineering majors (n = 592) include
                                 Liberal arts majors     Engineering majors
   X                             2.59                    2.29
   S                             1.00                    1.10

The smaller the mean, the more students agree with the statement. The formula
   for a t-test of mean differences for independent samples is




With         being the standard error of the mean difference




Where

Is a weighted average of sample standard deviations. In this situation the
    hypothesis:
               Essentials of Marketing Research        Kumar, Aaker, Day
Pooled Std. dev                                               = 1.07




                    Tts= 2.59-2.29 / .07 = .30 / .07 = 4.29



             Essentials of Marketing Research       Kumar, Aaker, Day
Statistical techniques

Analysis of Variance (ANOVA)


Correlation Analysis


Regression Analysis



      Essentials of Marketing Research   Kumar, Aaker, Day
      Analysis of Variance

• ANOVA mainly used for analysis of
  experimental data


• Ratio of “between-treatment” variance
  and “within- treatment” variance


  Essentials of Marketing Research   Kumar, Aaker, Day
 Analysis of Variance (ANOVA)
 Response        variable - dependent variable (Y)
 Factor(s)     - independent variables (X)
 Treatments    - different levels of factors
  (r1, r2, r3, …)




        Essentials of Marketing Research   Kumar, Aaker, Day
       One - Factor Analysis of Variance
   Studies the effect of 'r' treatments on one response variable
   Determine whether or not there are any statistically
    significant differences between the treatment means 1,
    2,... R
   Ho: all treatments have same effect on mean responses
   H1 : At least 2 of 1, 2 ... r are different




                Essentials of Marketing Research   Kumar, Aaker, Day
          Example (Book p.495)
                                             Product Sales
                 1            2              3      4      5               Total Xp
       39¢       8            12             10     9      11              50    10
Price
Level 44 ¢       7            10             6     8         9             40   8

       49 ¢      4            8              7     9         7             35   7

Overall sample mean: X = 8.333
Overall sample size: n = 15
No. of observations per price level: np = 5

          Essentials of Marketing Research             Kumar, Aaker, Day
Example (Book p.495)



                                                       Grand Mean




Essentials of Marketing Research   Kumar, Aaker, Day
           One - Factor ANOVA -
                 Intuitively
If:               Between Treatment Variance
        =
                  Within Treatment Variance

 is large then there are differences between treatments
 is small then there are no differences between
 treatments


     To Test Hypothesis, Compute the Ratio Between the
      "Between Treatment" Variance and "Within
      Treatment" Variance
           Essentials of Marketing Research   Kumar, Aaker, Day
        One - Factor ANOVA Table
Source of          Variation                Degrees of    Mean Sum           F-ratio
Variation          (SS)                     Freedom       of Squares

Between             SSr                     r-1           MSSr =SSr/r-1 MSSr
(price levels)                                                          MSSu

Within              SSu                     n-r           MSSu=SSu/n-r
(price levels)

Total               SSt                     n-1

                 Essentials of Marketing Research        Kumar, Aaker, Day
        One - Factor Analysis of Variance
   Between Treatment Variance
SSr =  np (Xp - X)2 = 23.3
         r

   Within-treatment variance
SSu =   (Xip - Xp)2 = 34
         np   r
Where   i=1 p=1
SSr = treatment sums of squares                  r = number of groups
np = sample size in group „p‟                    Xp = mean of group p

X = overall mean                                 Xip =sales at store i at level p

              Essentials of Marketing Research         Kumar, Aaker, Day
        One - Factor Analysis of
               Variance
 Between        variance estimate (MSSr)
  MSSr = SSr/(r-1) = 23.3/2 = 11.65


 Within     variance estimate (MSSu)
  MSSu = SSu/(n-r) = 34/12 = 2.8

Where
n = total sample size                       r = number of groups

         Essentials of Marketing Research     Kumar, Aaker, Day
         One - Factor Analysis of
                Variance
   Total variation (SSt): SSt = SSr + SSu = 23.3+34 = 57.3


   F-statistic: F = MSSr / MSSu = 11.65/2.8 = 4.16

   DF: (r-1), (n-r) = 2, 12

   Critical value from table: CV(, df) = 3.89




          Essentials of Marketing Research   Kumar, Aaker, Day