Question

If you select a very small value for $\mathit{\alpha }$when conducting a hypothesis test, will $\mathit{\beta }$ tend to be big or small? Explain.

Short answer

The lower values of significance level $\left(\alpha \right)$ increase the type II error $\left(\beta \right)$.

Step-by-step solution

Given information

The information regarding the values $\alpha$and $\beta$.

The level of significance, $\alpha$is small.

Define significance level and type II error probability

Type II error probability $\left(\beta \right)$:

The type II error probability $\beta$is calculated assuming that the null hypothesis is false because it is defined as the probability of accepting $H_0$when it is false.

i.e; $\beta =P(accept{H}_0/H_{0}isfalse0$

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

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.$\alpha =P(reject{H}_0/H_{0}istrue)$

Explain about  β when small value of  α conducting a hypothesis test

The type II error probabilityaccepts the null hypothesis when it is false. So, if a significance level is very small, then the region of acceptance expands. As a result, makes it difficult to reject the null hypothesis.

Therefore the lower values of significance level increase the type II error.