# At the .05 significance level, can we conclude that there is a difference in the

**Question description**

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 |
||||||

12.170 |
14.875 |
mean |
|||||

1.056 |
2.208 |
std. dev. |
|||||

10 |
12 |
n |
|||||

16 |
df |
||||||

-2.7050 |
difference (Prada - Oracle) |
||||||

0.7196 |
standard error of difference |
||||||

0 |
hypothesized difference |
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-3.76 |
t |
||||||

.0017 |
p-value (two-tailed) |
||||||

-4.2304 |
confidence interval 95.% lower |
||||||

-1.1796 |
confidence interval 95.% upper |
||||||

1.5254 |
margin of error |
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