Two boats the Prada Italy and the Oracle USA are competing f

Two boats, the Prada (Italy) and the Oracle (U.S.A.), are competing for a spot in the upcoming America\'s Cup race. They race over a part of the course several times. Below are a sample of times in minutes for each boat. Assume the population standard deviations are not the same. At the .05 significance level, can we conclude that there is a difference in their mean times?

Solution

Find : Prada sample mean time = 12.17; s = 1.056
& Oracle sample mean time = 14.875; s = 2.2079

A two sample t-test for means. Null hypothesis for this test would be that there is no difference in the mean times and the alternate hypothesis would be that there is a difference
Ho: u(Prada)-u(Oracle) = 0
Ha: u(P)-u(O) is not zero

Two-Sample Ttest on the data
test statistic: t= -3.76..
p-value = 0.0016..
df= 16.36

As  p is less than alpha=5%, reject Ho.
So, u(P) is not statistically the same as u(O)