Marketing Research

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Marketing Research

• Aaker, Kumar, Day
• Ninth Edition
• Instructors Presentation Slides

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Chapter Eighteen
Hypothesis Testing Means and Proportions
or
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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

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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

1. Formulate Hypotheses
2. Select appropriate formula
3. Select significance level
4. Calculate z or t statistic
5. Calculate degrees of freedom (for t-test)
6. Obtain critical value from table
7. 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 gt 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 gt tdf, ?/2 then reject
  Ho.

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Hypothesis Testing About A Single Mean - Example
3

• Ho ? ? 1000 (hypothesized value of population)
• Ha ? gt 1000 (alternative hypothesis)
• n 12
• X 1087.1
• s 191.6
• ? 0.05
• Rejection rule if tcalc gt tdf, ? then reject Ho.

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Confidence Intervals

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

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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

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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 Johns conversion ratio based on this
  sample of prospects
• qJ .16 Proportion that John failed to convert
• n1 100 Johns prospect sample size
• pL .82 Lindas conversion ratio based on her
  sample of prospects
• qL .18 Proportion that Linda failed to convert
• n2 100 Lindas prospect sample size

Null hypothesis Ho PJ P L Alternative
hypothesis Ha PJ ? PL Significance level a
.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
• 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 a 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
• 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
Observations Observations Observations Observations Observations Sample mean (Xp)
1 2 2 4 5 Total Sample mean (Xp)
39 8 12 10 9 11 50 10
44 7 10 6 8 9 40 8
49 4 8 7 9 7 35 7
Overall sample mean Xp 8.333 Overall sample
size n 15 No. of observations per price
level,n p5
Price Level
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Price Experiment ANOVA Table