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

Marketing ResearchAaker, Kumar, DayNinth EditionInstructor’s Presentation Slides

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

Chapter Eighteen

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Hypothesis Testing: Means and Proportions


Hypothesis Testing For Differences Between Means

• Commonly used in experimental research

• Statistical technique used is Analysis of Variance (ANOVA)

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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


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

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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

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Hypothesis Testing about a Single Mean – Step by Step

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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

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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 = 1087.1

• s = 191.6

• = 0.01

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

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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 = 1087.1

• s = 191.6

• = 0.05

Rejection rule: if tcalc > tdf, then reject Ho

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Confidence Intervals• Hypothesis testing and Confidence Intervals are two sides of the same coin.

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xs

Xt

)( of estimate interval xtsX


Procedure for Testing of Two Means

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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

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Po = .95: hypothesized value of the proportion of defect-free bulbsqo = .05: hypothesized value of the proportion of defective bulbsp = .87: sample proportion of defect-free bulbsq = .13: sample proportion of defective bulbs

Null hypothesis Ho: p = 0.95

Alternative hypothesis Ha: p ≠ 0.95Sample size n = 225Significance level = 0.05


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

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Hypothesis Testing of Difference between Proportions - Example

• Competition between sales reps, John and Linda for converting prospects to customers:

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Null hypothesis Ho: PJ = P L

Alternative hypothesis Ha : PJ ≠

PL

Significance level α = .05

PJ = .84 John’s conversion ratio based on this sample of prospectsqJ = .16 Proportion that John failed to convertn1 = 100 John’s prospect sample sizepL = .82 Linda’s conversion ratio based on her sample of prospectsqL = .18 Proportion that Linda failed to convertn2 = 100 Linda’s prospect sample size


Hypothesis Testing of Difference between Proportions – Example (contd.)

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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 0.0228 = 0.0456 (two-tailed test)

At α = 0.05, reject null hypothesis

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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, …)

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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

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Ho: all treatments have same effect on mean responses H1 : At least 2 of 1, 2 ... r are different


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

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One - Factor Analysis of Variance – Example

Observations Sample

mean

(Xp)

1 2 2 4 5 Total

39 ¢ 8 12 10 9 11 50 10

44 ¢ 7 10 6 8 9 40 8

49 ¢ 4 8 7 9 7 35 7

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Pri

ce L

evel Overall sample mean: Xp = 8.333

Overall sample size: n = 15No. of observations per price level,n p=5


Price Experiment ANOVA Table

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

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