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 33 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. Determine the null and alternative hypotheses that the magazine will test.

Answer 1

The null hypotheses that the magazine will test is
`H_(0) \geq 33`.

Alternative:
`H_(a) < 33`.

Explanation:

The null hypotheses is the one which contains the equal sign, while the alternative hypotheses is the opposite of the null hypotheses.

In this problem, we have that:

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 33 hours without​ oil, thanks to the engine treatment.

This means that at the very least, due to treatment, the engine should have lasted 33 hours. So the null hypotheses that the magazine will test is
`H_(0) \geq 33`.

Otherwise, the engine may have lasted less than 33 hours. So
`H_(a) < 33`.

Answer 2

Answer:
`H_0:\mu\geq33`

`H_a:\mu<33`

Explanation:

Let
`\mu` be the average number of hours a person drive without adding the product.

Given claim : An infomercial claims that a woman drove 33 hours without​ oil.

i.e.
`\mu\geq33`

It is known that the null hypothesis always contains equal sign and alternative hypothesis is just opposite of the null hypothesis.

Thus the null and alternative hypothesis for the given situation will be :-

`H_0:\mu\geq33`

`H_a:\mu<33`