Question on decision rule

[ajk003]

I'm a little confused on how to make a decision rule given an alpha value.
For example if the problem was a two ailed z test with a alpha of .03, what would I have to do to get the z value? Do I divide .03?

[JohnM]

Yes, divide .03 by 2 to get .015. In a two-tailed test, the probability that you incorrectly reject Ho (alpha) needs to be split up between the two tails, because you can be wrong in either direction.

[ajk003]

How would I find the probability of incorrectly rejecting the Ho? Would I have to look it up the z score chart? so for the problem above..the decision rule for a two tailed z test; alpha= .03 would be reject Ho at alpha= 0.03 if z is greater than or equal to 2.17???

[JohnM]

It's the same as alpha.

When alpha is set to a particular value, this is the level of "risk" you are willing to take when rejecting Ho. A very low level of alpha, say .001, means that you are looking for a relatively large z score (positive or negative), which correlates with "a lot of evidence against Ho."

In other words, with alpha = .001 you want to be "really sure" or 99.9% sure (sure = "confidence level") that Ho is not true.

Yes, a z-score of 2.17 or -2.17 would be required to reject Ho with a two-tailed test and alpha set at .03.

With alpha set at .03, if you get a z-score outside of 2.17 or -2.17, then you can reject Ho with a 97% confidence level.