Question

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 the sample times in minutes. Assume the population standard deviations are the same.

At the .10 significance level, can we conclude that there is a difference in their mean times? Assume the population variances are equal.

Prada-12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, 11.3

Oracle- 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, 19.0

The computed test statistic for the sample above is ________ (round to 4 decimals). Note: compute the test statistic in the order of how the groups appear on the hypotheses.

At the 0.10 significance level, what is the critical value for testing the null hypothesis? _________

What is the p-value for the test? _____________ (round to 4 decimals).

At the 0.10 significance level, what is the correct statistical conclusion?

a.Reject the null hypothesis

b.Fail to reject the null hypothesis

c.Reject the alternate hypothesis

d.Fail to reject the alternate hypothesis

e.None of the above. The test is inconclusive

Based on the result of the statistical test above, which of the following would be the correct conclusion?

a.There is no difference in the average time of the two boats.

b.There is a difference in the average time of the two boats – Prada is faster.

c.There is a difference in the average time of the two boats – Oracle is faster.

d.There is not enough data to make a conclusion.

e.None of the above

Answer 1

The statistical software output for this problem is:

Two sample T hypothesis test:
?₁ : Mean of Prada
?₂ : Mean of Oracle
?₁ - ?₂ : Difference between two means
H₀ : ?₁ - ?₂ = 0
H_A : ?₁ - ?₂ ? 0
(with pooled variances)

Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
?1 - ?2	-2.705	0.76392544	20	-3.5409215	0.0021

Hence,

Test statistic = -3.5409

Critical value = -1.7247, 1.7247

p - Value = 0.0021

Correct statistical conclusion: Reject the null hypothesis

Correct conclusion: There is a difference in the average time of the two boats – Prada is faster.