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

2. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Chapter Eighteen 2 Hypothesis Testing: Means and Proportions

3. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing For Differences Between Means Commonly used in experimental research Statistical technique used is Analysis of Variance (ANOVA) 3 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

4. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ 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 h o accordingly Using the p-value: ▫Researcher determines "how unlikely is the result that has been observed?" ▫Decide whether to reject or fail to reject h o without being bound by a pre-specified significance level 4

5. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ 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 h o 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 5

6. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing about a Single Mean – Step by Step Make decision regarding the Null-hypothesis Obtain critical value from table Calculate degrees of freedom (for t-test) Calculate z or t statistic Select significance level Select appropriate formula Formulate Hypotheses 6

7. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing About A Single Mean - Example 1 - Two-tailed test H o :  = 5000 (hypothesized value of population) H a :   5000 (alternative hypothesis) n = 100 X = 4960  = 250  = 0.05 Rejection rule: if |z calc | > z  /2 then reject H o 7

8. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing About A Single Mean - Example 2 H o :  = 1000 (hypothesized value of population) H a :   1000 (alternative hypothesis) n = 12 X = 1087.1 s = 191.6  = 0.01 Rejection rule: if |t calc | > t df,  /2 then reject H o 8

9. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing About A Single Mean - Example 3 H o :   1000 (hypothesized value of population) H a :  > 1000 (alternative hypothesis) n = 12 X = 1087.1 s = 191.6  = 0.05 Rejection rule: if t calc > t df,  then reject H o 9

10. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Confidence Intervals Hypothesis testing and Confidence Intervals are two sides of the same coin. 10

11. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Procedure for Testing of Two Means 11

12. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ 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 12 P o =.95: hypothesized value of the proportion of defect-free bulbs q o =.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 H o : p = 0.95 Alternative hypothesis H a : p ≠ 0.95 Sample size n = 225 Significance level = 0.05

13. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing of Proportions – Example (Contd.) Standard error = Using Z-value for.95 as 1.96, the limits of the acceptance region are Therefore, Reject Null hypothesis 13

14. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing of Difference between Proportions - Example Competition between sales reps, John and Linda for converting prospects to customers: 14 Null hypothesis H o : P J = P L Alternative hypothesis H a : P J ≠ P L Significance level α =.05 P J =.84 John’s conversion ratio based on this sample of prospects q J =.16 Proportion that John failed to convert n 1 = 100 John’s prospect sample size p L =.82 Linda’s conversion ratio based on her sample of prospects q L =.18 Proportion that Linda failed to convert n 2 = 100 Linda’s prospect sample size

15. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Hypothesis Testing of Difference between Proportions – Example (contd.) 15

16. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Probability –Values Approach to Hypothesis Testing Example: ▫Null hypothesis H 0 : µ = 25 ▫Alternative hypothesis H a : µ ≠ 25 ▫Sample size n = 50 ▫Sample mean X =25.2 ▫Standard deviation = 0.7 Standard error = Z- statistic = P-value = 2 X 0.0228 = 0.0456 (two-tailed test) At α = 0.05, reject null hypothesis 16

17. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ 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 (r 1, r 2, r 3, …) 17

18. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ 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 18 H o : all treatments have same effect on mean responses H 1 : At least 2 of  1,  2...  r are different

19. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ 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 19

20. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ One - Factor Analysis of Variance – Example Observations Sample mean (X p ) 12245Total 39 ¢812109115010 44 ¢710689408 49 ¢48797357 20 Price Level Overall sample mean: X p = 8.333 Overall sample size: n = 15 No. of observations per price level,n p =5

21. Marketing Research 10th Edition http://www.drvkumar.com/mr10/ Price Experiment ANOVA Table 21