Question

2. what is the p-value for an observed z0= -2.54 fora two tailed test? show your work and illustration

3. what happens to the probability of type 1 error as the probability of type II error increases?

Answer 1

Answer 2

We need to find the p value corresponding to z score value of -2.54

First, we will find the left tailed value, then multiply that value by 2 to get the two tailed hypothesis

Using z distribution table, check -2.5 in the left most column and check 0.04 in the top most row, then select the intersecting cell

this cell value using z distribution table is 0.0055

Now, multiply it by 2

this gives us, p value = 2*0.0055 = 0.0110

So, required p value is 0.0110

Answer 3

We know that probability of type I error and type II error are inversely proportional, i.e. when one probability increases, other probability decreases or vice versa.

So, when the probability of type II error increases, then the probability of type I error will decrease.