Posted: December 18th, 2015
Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race.
1.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.
| Hypothesis Test: Independent Groups (t-test, unequal variance) | ||
| Prada | Oracle | |
| 12.17 | 14.875 | mean |
| 1.056 | 2.208 | std. dev. |
| 10 | 12 | n |
| 16 | df | |
| -2.705 | difference (Prada – Oracle) | |
| 0.7196 | standard error of difference | |
| 0 | hypothesized difference | |
| -3.76 | t | |
| 0.0017 | p-value (two-tailed) | |
| -4.2304 | confidence interval 95.% lower | |
| -1.1796 | confidence interval 95.% upper | |
| 1.5254 | margin of erro | |
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