Question

The car manufacturer Lamborghini claims that its high-performance sports car, the Lamborghini Aventador, has an average top speed exceeding 220 mph. A car enthusiast tests this claim by renting 14 of the vehicles and recording their top speed. He finds that the average top speed of the sample is 218mph, with a sample standard deviation of 3mph. For the test, the car enthusiast determines that α = 0.10

Write the null and alternative hypotheses. Is this a left, right, or two-tailed test?

Calculate the standard error of the sample.

Suppose the car enthusiast calculates the rejection region by finding the t-score that delivers a p-value of 0.10(known as the critical value): t = -1.35→ p-value = 0.10

Calculate the t-score of the sample.

In two sentences, what should the car enthusiast conclude from this hypothesis test? Then, in one sentence, explain how you came to this decision.

Answer 1

Let denotes the average top speed.

This is a right tailed test.

Conclusion : There is not enough evidence to support the claim that its high-performance sports car, the Lamborghini Aventador, has an average top speed exceeding 220 mph.