Marketing Research

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

Chapter Eighteen Hypothesis Testing: Means and Proportions or http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

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. http://www.drvkumar.com/mr9/

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. http://www.drvkumar.com/mr9/

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. http://www.drvkumar.com/mr9/

Confidence Intervals • Hypothesis testing and Confidence Intervals are two sides of the same coin.  interval estimate of  http://www.drvkumar.com/mr9/

Procedure for Testing of Two Means http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

Hypothesis Testing of Difference between Proportions – Example (contd.) http://www.drvkumar.com/mr9/

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 0.0228 = 0.0456 (two-tailed test) At α = 0.05, reject null hypothesis http://www.drvkumar.com/mr9/

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, …) http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

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 http://www.drvkumar.com/mr9/

One - Factor Analysis of Variance – Example Overall sample mean: Xp = 8.333 Overall sample size: n = 15 No. of observations per price level,n p=5 Price Level http://www.drvkumar.com/mr9/

Price Experiment ANOVA Table http://www.drvkumar.com/mr9/

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