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Unformatted text preview: are the p-value with α.
If p-value < α : Reject the H0 . You have enough evidence that H0 is false.
If p-value > α : Fail to reject H0 . There is not enough evidence to reject the null hypothesis. In our example, we reject the null if α is set to be 0.05 or 0.1 but not if 0.01. p-value approach
allows easy comparison of decision with diﬀerent α’s. Notice: p-value is the smallest α choice
where H0 is rejected. Utku Suleymanoglu (UMich) Hypothesis Testing 14 / 39 Testing Hypothesis about the Population Mean: Case 1 σ known Critical Value Approach for One-Tailed Tests Another equivalently valid approach to create to criteria for testing would be this:
1. After hypotheses statement and the calculation of test statistic (z for this case).
2. Set an α. Say, α = 0.05.
3. Figure out the zα such that P (Z ≥ zα ) = α: The z-value with upper-tail probability of α.
4. Make a decision about H0 by comparing the test statistic with a critical value. Critical value
tells us which values are too far oﬀ from the null hypothesis value.
Left-tailed tests: Reject H0 if z < −zα . Critical value= −zα
Right-tailed tests: Reject H0 if z > zα . Critical value= zα 5. Choosing an α and ﬁnding the critical value creates a rejection region. If the test statistic is
in this region, H0 is rejected.
The key idea: Instead of comparing probability with a small enough probability (α), choose α
ﬁrst and establish a far enough test statistic. Utku Suleymanoglu (UMich) Hypothesis Testing 15 / 39 Testing Hypothesis about the Population Mean: Case 1 σ known Example Cont. For our example, critical value with α = 0.05 is −1.645 = −zα .
Then any test static which is smaller than than −1.645 is in the rejection region.
We had z = −1.66, so we reject the the null hypothesis. 0 z Exercise: Calculate the largest x value which will lead to the rejection of the null.
¯ Utku Suleymanoglu (UMich) Hypothesis Testing 16 / 39 Testing Hypothesis about the Population Mean: C...
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This note was uploaded on 03/17/2014 for the course ECON 404 taught by Professor Staff during the Spring '08 term at University of Michigan.
- Spring '08