Type of Hypothesis Test to be Used

[3.141592654]

Problem Statement

In the production of airbag inflators for automotive safety systems, a company is interested in ensuring that the mean distance is at least 2.00 cm. Measurements on 20 inflators yielded an average value of 2.02 cm. The sample standard deviation is .05 on the distance measurements and use a significance level of .01.

Attempted Solution

This is a problem that my class worked through in lecture, so I'm not looking for the answer. Instead, I'm trying to determine why the following hypothesis test was used by my professor:

$H_{0}: \mu = 2.00 cm$
$H_{0}: \mu > 2.00 cm$

My interpretation of the problem is that some company needs to ensure that $\mu \geq$2.00 cm. So by doing the hypothesis test outlined above we'll either conclude the mean is 2.00 cm or it is greater than 2.00 cm, which are both equally acceptable to the company. The alternative scenario, that the mean is less than 2.00 cm, isn't tested. But that's what the company needs to worry about. So shouldn't we test:

$H_{0}: \mu = 2.00 cm$
$H_{0}: \mu < 2.00 cm$

?

Thanks.

 

[Stephen Tashi]

You need an $H_1$.

Statistics is subjective. The hope of the company is presumably to offer strong evidence that $\mu \ge 2.0$. If they test for $\mu \lt 2.0$ it's as if they are saying "Go ahead. Let's see if you can prove $\mu \lt 2.0$". That doesn't inspire confidence in the consumer who buys the airbag inflator. Compare which side of the question gets the benefit of the doubt if the result is only significant at the 0.05 level.