Question

If the rejection of the null hypothesis of a particular test would cause your firm to go out of business, would you want $\mathit{a}$to be small or large? Explain

Short answer

The firm would want $a$ to be small.

Step-by-step solution

Given information

The rejection of the null hypothesis of a particular test would cause a firm to go out of business.

State level of significance

Significance level $\left(a\right)$:

The level of significance is the size of the type I error. In other words, rejecting the null hypothesis when it is true.

i.e.,$a=P(reject{H}_0/H_{0}istrue)$

Explain about the a, is small or large

If a null hypothesis rejection resulted in a farm going out of business, that firm would put in significant effort ensuring that it does not falsely identify a null hypothesis as correct. So, which is a type I error. Since, $a$ symbolizes this type I error.

Hence, the firm would want $a$ to be small.