Example 10.1a Experimenting with a New Pizza Style at the Pepperoni Pizza Restaurant

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Example 10.1aExperimenting with a New Pizza
Style at the Pepperoni Pizza Restaurant

• Hypothesis Tests for a Population Mean

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Objective
To use a one-sample t test to see whether
consumers prefer the new style pizza to the old
style.
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Background Information

• Recall that the manager of the Pepperoni Pizza
  Restaurant is running an experiment to test the
  hypotheses of H0 mu ? 0 versus Ha mugt 0, where
  mu is the mean rating in the entire customer
  population.
• Here, each customer rates the difference between
  an old-style pizza and a new-style pizza on a
  -10 to 10 scale, where negative ratings favor
  the old-style pizza and positive ratings favor
  the new-style pizza.

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PIZZA.XLS

• The ratings of 40 randomly selected customers and
  several summary statistics appear in this file
  and in the following table.

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Summary Statistics

• From the summary statistics, we see that the
  sample mean is 2.10 and the sample standard
  deviation is 4.717.
• The positive sample mean provides some evidence
  in favor of the alternative hypothesis, but given
  the rather large standard deviation and the
  boxplot of ratings shown on the next slide does
  it provide enough evidence to reject H0?

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Summary Statistics -- continued
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Running the Test

• To run the test, we calculate the test statistic,
  using the borderline null hypothesis value mu0
  0, and report how much probability is beyond it
  in the right tail of the appropriate t
  distribution.
• We use the right tail because the alternative is
  one-tailed of the greater than variety.
• The test statistic is

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Running the Test -- continued

• The probability beyond this value in the right
  tail of the t distribution with n-1 39 degrees
  of freedom is approximately 0.004, which can be
  found in Excel with the function
  TDIST(2.816,39,1).
• The probability, 0.004, is the p-value for the
  test. It indicates that these sample results
  would be very unlikely if the null hypothesis is
  true.
• The manager has two choices he can conclude that
  the null hypothesis is true or he can conclude
  that the alternative hypothesis is true - and
  presumably switch to the new-style pizza. The
  second choice appears to be more reasonable.

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Using StatPro

• Another way to interpret the results is in terms
  of traditional significance levels but the
  p-value is the preferred method.
• The StatPro One-Sample procedure can be used to
  perform this analysis easily. To use it select
  the StatPro/Statistical Inference/One-Sample
  Analysis menu item, and choose the Rating
  variable as the variable to analyze.
• Then fill in the dialog boxes as shown here.

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One-Sample Dialog Box
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Hypothesis Test Dialog Box
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The Results

• Most of this output should be familiar it
  mirrors the previous calculations.
• The results are significant at the 1 level.

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Conclusion

• Should the manager switch to the new-style pizza
  on the basis of these sample results?
• We would probably recommend yes. There is no
  indication that the new-style pizza costs any
  more to make than the old-style pizza, and the
  sample evidence is fairly convincing that
  customers, on average, will prefer the new-style
  pizza.
• Therefore, unless there are reasons for not
  switching (for example, costs) then we recommend
  the switch.