# Calculating the size of Type 1 error, Type 2 error and power of the test

#### Cynderella

##### New Member
Let $$X$$ have a binomial distribution with parameter $$n=5$$ and $$P\in [p=\frac{1}{4},\frac{1}{2}]$$.

The null hypothesis $$H_{0}=\frac{1}{4}$$ is rejected, and The alternative hypothesis $$H_a=\frac{1}{2}$$ is accepted.

If the observed value of $$X_1$$, a random sample of size one, is less than or equal to $$3$$.

Find the size of Type 1 error, Type 2 error and power of the test.

I have no idea to solve the question. I only know that

###Size of a Type 1 error = Pr[rejecting$$H_0|H_0$$is true]
###Size of a Type 2 error = Pr[not rejecting[/math]H_0|H_0 [/math]is False]

The sign $$|$$ denotes "given that".

#### rogojel

##### TS Contributor
hi,
this looks like homework and you need to show a credible effort to get help.

You are given a decision rule ( lines 2 and 3 in your post) so you can define the event of rejecting/accepting H0 in terms of your decision rule. Once you have that, calculating the probabilities is easy.

BTW the rule you gave does not make sense to me. Are you sure it is " less then" not greater then?

regards
rogojel

#### Cynderella

##### New Member
BTW the rule you gave does not make sense to me. Are you sure it is " less then" not greater then?
This question is an exam question of previous year and there it is " less then".

regards
Cynderella