Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America's Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were: 12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t-Test: Two-Sample Assuming Unequal Variances.
The next table shows the results of this independent t-test. At the .05 significance level, can we conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means.
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Hypothesis Test: Independent Groups (t-test, unequal variance)
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Prada
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Oracle
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12.17
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14.875
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mean
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1.056
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2.208
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std. dev.
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10
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12
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n
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16
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df
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-2.705
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difference (Prada - Oracle)
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0.7196
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standard error of difference
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0
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hypothesized difference
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-3.76
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t
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0.0017
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p-value (two-tailed)
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-4.2304
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confidence interval 95.% lower
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-1.1796
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confidence interval 95.% upper
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1.5254
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margin of error
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