Question

The manufacturer of a certain engine treatment claims that if you add their product to your​ engine, it will be protected from excessive wear. An infomercial claims that a woman drove 6 hours without​ oil, thanks to the engine treatment. A magazine tested engines in which they added the treatment to the motor​ oil, ran the​ engines, drained the​ oil, and then determined the time until the engines seized. Complete parts ​(a) and ​(b) below. ​(a) Determine the null and alternative hypotheses that the magazine will test. Upper H 0​: mu equals 6 Upper H 1​: mu less than 6 ​(b) Both engines took exactly 11 minutes to seize. What conclusion might the magazine make based on this​ evidence? A. The​ infomercial's claim is not true. B. The​ infomercial's claim is true.

Answer 1

Answer: (a)Null hypothesis: $H_0:\mu=6$

Alternative hypothesis: $H_a:\mu<6$

(b) Conclusion: A. The​ infomercial's claim is not true.

Explanation:

Let $\mu$ be the mean number of hours drove without​ oil .

(a) Since the woman drove 6 hours without​ oil because of the engine treatment.

We expect that this is too high to drive without oil

So, the hypothesis in this case would be

Null hypothesis: $H_0:\mu=6$

Alternative hypothesis: $H_a:\mu<6$

(b) 11 minutes is much lower than 6 hours.

That means it supports the alternative hypothesis.

Conclusion: A. The​ infomercial's claim is not true.