Transcript Example 10.1a

Example 10.1a
Experimenting with a New Pizza Style at
the Pepperoni Pizza Restaurant
Hypothesis Tests for a Population
Mean
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: mu> 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 onetailed of the “greater than” variety.

The test statistic is
t  value 
2.10  0
4.717 / 40
 2.816
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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.
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