1. Aaker, Kumar, Day Ninth Edition Instructor’s Presentation Slides
Marketing Research
Aaker, Kumar, Day
Ninth Edition
Instructor’s Presentation Slides

2. Hypothesis Testing: Means and Proportions
Chapter Eighteen
Hypothesis Testing:
Means and Proportions or
Marketing Research 9th Edition
Aaker, Kumar, Day

3. 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 or not known
If the population standard deviation is not known, whether they
can be assumed to be equal or not
Marketing Research 9th Edition
Aaker, Kumar, Day

4. The Probability Values (p-value) Approach to Hypothesis Testing
Difference between using  and p-value
Hypothesis testing with a pre-specified 
Researcher determines "is the probability of what has been observed less than ?"
Reject or fail to reject ho accordingly
Using the p-value:
Researcher determines "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
Marketing Research 9th Edition
Aaker, Kumar, Day

5. The Probability Values (P-value) Approach to Hypothesis Testing (Contd
p-value provides researcher with alternative method of testing hypothesis without pre-specifying 
p-value is the largest level of significance at which we would not reject ho
In general, the smaller the p-value, the greater the 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
Marketing Research 9th Edition
Aaker, Kumar, Day

6. Hypothesis Testing About A Single Mean – Step by-Step
Formulate Hypotheses
Select appropriate formula
Select significance level
Calculate z or t statistic
Calculate degrees of freedom (for t-test)
Obtain critical value from table
Make decision regarding the Null-hypothesis
Marketing Research 9th Edition
Aaker, Kumar, Day

7. Hypothesis Testing About A Single Mean - Example 1 - Two-tailed test
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.
Population case: therefore z-test
Standard error of mean: x =  /sqrt(n) = 250/10 = 25
z= ( ) / 25 = -1.6
z/2 = 1.96
if |zcalc| > z/2 then reject Ho
since |-1.6| < do not reject Ho.
Marketing Research 9th Edition
Aaker, Kumar, Day

8. Hypothesis Testing About A Single Mean - Example 2
Ho:  = 1000 (hypothesized value of population)
Ha:   1000 (alternative hypothesis)
n = 12
X =
s = 191.6
 = 0.01
Rejection rule: if |tcalc| > tdf, /2 then reject Ho.
Softdrink manufacturer plans to introduce new soft drink. 12 supermarkets are selected at random and soft drink is offered in these supermarkets for limited time.Average existing softdrink sales are 1000, new softdrink sales are
Sample < 60 therefore t-test
Standard error of mean: sx = s /sqrt(n) = 191.6/sqrt(12) = 55.31
tcalc= ( ) / = 1.57
df = 12-1 = 11
t11,/2 = 3.106
if |tcalc| > t/2 then reject Ho
since |1.57| < do not reject Ho.
Marketing Research 9th Edition
Aaker, Kumar, Day

9. Hypothesis Testing About A Single Mean - Example 3
Ho:   1000 (hypothesized value of population)
Ha:  > 1000 (alternative hypothesis)
n = 12
X =
s = 191.6
 = 0.05
Rejection rule: if tcalc > tdf,  then reject Ho.
One sided test
Sample < 30 therefore t-test
Standard error of mean: x =  /sqrt(n) = 191.6/sqrt(12) = 55.31
tcalc= ( ) / = 1.57
df = 12-1 = 11
t11,/2 = 1.796
if tcalc > t then reject Ho
since 1.57 < do not reject Ho.
Rejection rule for opposite directionality:
if tcalc < -t then reject Ho
Marketing Research 9th Edition
Aaker, Kumar, Day

10. Confidence Intervals
Hypothesis testing and Confidence Intervals are two sides of the same coin.
 interval estimate of 
Marketing Research 9th Edition
Aaker, Kumar, Day

11. Procedure for Testing of Two Means
Marketing Research 9th Edition
Aaker, Kumar, Day

12. Hypothesis Testing of Proportions - Example
CEO of a company finds 87% of 225 bulbs to be defect-free
To Test the hypothesis that 95% of the bulbs are defect free
Po = .95: hypothesized value of the proportion of defect-free bulbs
qo = .05: hypothesized value of the proportion of defective bulbs
p = .87: sample proportion of defect-free bulbs
q = .13: sample proportion of defective bulbs
Null hypothesis Ho: p = 0.95
Alternative hypothesis Ha: p ≠ 0.95
Sample size n = 225
Significance level = 0.05
Marketing Research 9th Edition
Aaker, Kumar, Day

13. Hypothesis Testing of Proportions – Example (contd. )
Standard error =
Using Z-value for .95 as 1.96, the limits of the acceptance region are
Reject Null hypothesis
Marketing Research 9th Edition
Aaker, Kumar, Day

14. Hypothesis Testing of Difference between Proportions - Example
Competition between sales reps, John and Linda for converting prospects to customers:
PJ = .84 John’s conversion ratio based on this sample of prospects
qJ = .16 Proportion that John failed to convert
n1 = 100 John’s prospect sample size
pL = .82 Linda’s conversion ratio based on her sample of prospects
qL = .18 Proportion that Linda failed to convert
n2 = 100 Linda’s prospect sample size
Null hypothesis Ho: PJ = P L
Alternative hypothesis Ha : PJ ≠ PL
Significance level α = .05
Marketing Research 9th Edition
Aaker, Kumar, Day

15. Hypothesis Testing of Difference between Proportions – Example (contd
Marketing Research 9th Edition
Aaker, Kumar, Day

16. Probability –Values Approach to Hypothesis Testing
Example:
Null hypothesis H0 : µ = 25
Alternative hypothesis Ha : µ ≠ 25
Sample size n = 50
Sample mean X =25.2
Standard deviation = 0.7
Standard error =
Z- statistic =
P-value = 2 X = (two-tailed test)
At α = 0.05, reject null hypothesis
Marketing Research 9th Edition
Aaker, Kumar, Day

17. Analysis of Variance
ANOVA mainly used for analysis of experimental data
Ratio of “between-treatment” variance and “within- treatment” variance
Response variable - dependent variable (Y)
Factor (s) - independent variables (X)
Treatments - different levels of factors (r1, r2, r3, …)
Marketing Research 9th Edition
Aaker, Kumar, Day

18. 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
Marketing Research 9th Edition
Aaker, Kumar, Day

19. One - Factor Analysis of Variance (contd.)
Between-treatment variance - Variance in the response variable for different treatments.
Within-treatment variance - Variance in the response variable for a given treatment.
If we can show that ‘‘between’’ variance is significantly larger than the ‘‘within’’ variance, then we can reject the null hypothesis
Marketing Research 9th Edition
Aaker, Kumar, Day

20. One - Factor Analysis of Variance – Example
Observations
Sample mean (Xp) 1 2 4 5
Total
39 ¢ 8 12 10 9 11 50
44 ¢ 7 6 40
49 ¢ 35
Overall sample mean: Xp = 8.333
Overall sample size: n = 15
No. of observations per price level,n p=5
Price Level
Marketing Research 9th Edition
Aaker, Kumar, Day

21. Price Experiment ANOVA Table
Marketing Research 9th Edition
Aaker, Kumar, Day