Type II Error Rate Question?

I can't seem to figure out how to obtain the type 2 error rate from this question.

A researcher is conducting a hypothesis test to determine whether people can be trained to be better at detecting when someone's lying. He found training on average an increase in probability of detection by 0.06, data's normally distributed and standard error of training effect of the population is 0.135. If type I error rate is 0.05 what's your type II error rate?

Any help greatly appreciated! Thank you

Re: Type II Error Rate Question?

Hey Donmarco.

The first thing you should look at is what the definition is. We know Type I error is P(H1 retained|H0 correct) while Type II is P(H0 retained|H1 correct) = 1 - P(H1 retained|H1 correct).

So now we need to know what the hypotheses are to get a specific value: what are your hypotheses for this particular example?

Re: Type II Error Rate Question?

Thanks Chiro

I started using this hypothesis H0: p ≥ 0.06 vs. H1: p < 0.06 I assume its right, this is still quite new to me

Re: Type II Error Rate Question?

Re: Type II Error Rate Question?

Hi Donmarco! :)

To calculate a type II error, you need knowledge about the actual alternative population.

In the problem it is given that the alternative population has an average that is 0.06 greater than the null population.

Let's call $\displaystyle \pi$ the chance that someone detects a lie after training. This is what is measured.

Actually, it's he proportion of successful detections that is counted.

We'll call that measured proportion $\displaystyle p$.

Let's call $\displaystyle \pi_0$ the average chance that someone detects a lie.

And let's call $\displaystyle \pi_1$ the average chance that someone detects a lie after training.

From the problem statement, we can say that $\displaystyle \pi_1 = \pi_0 + 0.06$.

The null hypothesis is:

H0: training does not help, or $\displaystyle \pi = \pi_0$

H1: training does help, or $\displaystyle \pi > \pi_0$

Now, what is the critical value $\displaystyle p_{crit}$ that we need to say with at least 95% certainty that training helps?

And since we already know the actual alternative population, what is the chance that H0 is retained even while knowing that H1 is true ($\displaystyle \pi = \pi_0 + 0.06$)?

This latter chance is the type II error.