National open university of nigeria introduction to econometrics I eco 355

7. Evaluate Null Hypothesis
:
We calculate Z and then look up the P value for the obtained Z, and make a decision. 
Here's what happens:
The P value is way below .00001, so we reject the null hypothesis that there is an 
unrestrictive selection process for admitting students to UNC. We conclude that the 
selection process results in Math SAT scores for UNC students that are higher than the 
population as a whole.
 
 
8. Statistical Power

---

110 
As we have seen, hypothesis testing is about seeing if a particular treatment has an effect. 
Hypothesis testing uses a framework based on testing the null hypothesis that there is no 
effect. The test leads us to decide whether or not to reject the null hypothesis.
We have examined the potential for making an incorrect decision, looking at Type I and 
Type II errors, and the associated significance level for making a Type I error.
We now reverse our focus and look at the potential for making a correct decision. This is 
referred to as the power of a statistical test. 
However, the power of a statistical test is the probability that the test will correctly reject 
a false null hypothesis. The more powerful the test is, the more likely it is to detect a 
treatment effect when one really exists.
9. Power and Type II errors
:
When a treatment effect really exists the hypothesis test:
(i). can fail to discover the treatment effect (making a Type II error). The 
probability of this happening is denoted:
= 
P
[Type II error]
(ii)
can correctly detect the treatment effect (rejecting a false null 
hypothesis). The probabililty of this happening, which is the power of 
the test, is denoted:
= power = 
P
[rejecting a false Ho].
Here is a table summarizing the Power and Significance of a test and their relationship to 
Type I and II errors and to "alpha" and "beta" the probabilities of a Type I and Type II 
error, respectively: