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Exercises 12-15 thru 12-17. Textbook PDF's with questions omitted for copyright reasons. Refer to attachments for necessary data.

Please begin each solution by stating or restating the problem, establishing parameters, establishing the hypothesis, defining parameters used, and ending with both the statistical decision and business decision reached by the analysis.

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The expert examines hypothesis and defining parameters.

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Solution-12.15:
a)
Null and Alternate Hypothesis:
Null Hypothesis: The mean operating cost per mile for all the three types of minivans are the same.
Alternate Hypothesis: At least one of the minivans has a significantly different mean operating cost per mile.

Analysis Plan: We shall use ANOVA to test the given hypothesis. The chosen level of significance for the given hypothesis test is 0.05.

Calculation of F-Statistic:
The F-statistic has been calculated using Excel's Data Analysis.
ANOVA: Single Factor
SUMMARY
Groups Count Sum Average Variance
Mini 1 5 68 13.600 0.3450
Mini 2 3 38.9 12.967 0.2633
Mini 3 4 59.1 14.775 0.5158

Source of Variation SS df MS F P-value F critical
Between Groups 6.0725 2 3.03625 7.911097708 0.010406638 4.25649
Within Groups 3.454167 9 0.383796296
Total 9.526667 11
t-Critical 2.262157

Multiple Comparisons LSD Fisher Test Calculations:

Comparison Difference LSD Lower Conf. Limit. Upper Conf. Limit Significant or Not Significant
Mini 1 - Mini 2 0.633 0.45 0.10 1.16 Significant
Mini 2 - Mini 3 1.808 0.47 1.25 2.36 Significant
Mini 3 - Mini 1 1.175 0.42 0.69 1.66 Significant

Interpretation of results:
As we can see, the mean operating costs per mile for all the three types of minivans are different. But are these differences statistically significant?
The decision rule for rejecting the null hypothesis is given as:

According to the test result p-value = 0.010, which is smaller than the level of significance.
Thus, we ...

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Anwesha Ghosh, MSc
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  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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