Transcript Marketing Research

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Marketing Research
Aaker, Kumar, Day
Ninth Edition
Instructor’s Presentation Slides
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Chapter Eighteen
Hypothesis Testing:
Means and Proportions
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Hypothesis Testing For
Differences Between Means
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Commonly used in experimental research
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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
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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
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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
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
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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.
(X  )
t
sx
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X  tsx  interval estimate of 
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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 defectfree
• To Test the hypothesis that 95% of the bulbs are defect
free
Po
qo
p
q
= .95: hypothesized value of the proportion of defect-free bulbs
= .05: hypothesized value of the proportion of defective bulbs
= .87: sample proportion of defect-free bulbs
= .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
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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
• 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:
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
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Hypothesis Testing of Difference between
Proportions – Example (contd.)
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Probability –Values Approach to Hypothesis Testing
• Example:
▫ Null hypothesis H0 : µ = 25
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▫
▫
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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 “withintreatment” 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
Ho: all treatments have same effect on mean responses
H1 : At least 2 of 1, 2 ... r are different
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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
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One - Factor Analysis of Variance – Example
Price Level
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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Overall sample mean: Xp = 8.333
Overall sample size: n = 15
No. of observations per price level,n p=5
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Price Experiment ANOVA Table
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