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**Aaker, Kumar, Day Ninth Edition Instructor’s Presentation Slides**

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

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**Hypothesis Testing: Means and Proportions**

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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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

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**Procedure for Testing of Two Means**

Marketing Research 9th Edition Aaker, Kumar, Day

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**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

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**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

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**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

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**Hypothesis Testing of Difference between Proportions – Example (contd**

Marketing Research 9th Edition Aaker, Kumar, Day

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**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

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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

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**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

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**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

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**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

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**Price Experiment ANOVA Table**

Marketing Research 9th Edition Aaker, Kumar, Day

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