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

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 as follows: 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 as follows: 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 you 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 who 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

-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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