1. Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming Americas 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 Americas 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
