6 is not the case lets see what we are doing on a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 39 What determines test results? This time lets start with the Critical Value Approach: After stating the hypotheses and calculating the z-statistic, the decision rule is going to be: x −µ ¯ Reject H0 if | σ/√0 | > zα/2 n In other words, reject the null if the test statistic is outside the interval (−zα/2 , zα/2 ) where critical value zα/2 is the z-value for upper tail probability α/2. For our example, we have z = 2.5−2.6 √ 1/ 25 = 0.1/0.3 = −0.33. Let’s pick α = 0.05, then α/2 = 0.025 and zα/2 = 1.96. Because z = 0.33 lies inside the interval (−1.96, 1.96), we do not reject the null hypothesis. We don’t have enough evidence to assert that µ = 2.6 is not the case. Let’s see what we are doing on a picture. Utku Suleymanoglu (UMich) Hypothesis Testing 24 / 39 What determines test results? Graphical Explanation 0 Utku Suleymanoglu (UMich) Hypothesis Testing z 25 / 39 What determines test results? p-value Approach for Two-Tailed Tests We can also calculate a p-value for the test statistic z , to compare with different α’s to get a conclusion. The p-value can be calculated as the area outside the interval (−z , z ), or simply (due to symmetricity) as 2 × P (Z > z = 0.33) In our example we get a p-value 2 × P (Z > z = 0.33) = 2 × 0.3707 = 0.7414. This value is bigger than any reasonable α so reach at the same conclusion as before. We fail to reject the null hypothesis. Let’s go back one slide and see this on a picture. Utku Suleymanoglu (UMich) Hypothesis Testing 26 / 39 What determines test results? Hypothesis Testing Fundamentals Recap Before we go on to different cases, let’s repeat the general idea of hypothesis testing: We have an hypothetical value for a population parameter (µ = µ0 ) as a claim and we want to test this. We have a sample and a point estimate x = 2, let’s say. ¯ We know the sampling distribution of x assuming the claim is true from chapter 6. ¯ Then we can evaluate the probability of x or a similar draw from this sampling distribution. ¯ To do that we need to transform our normal random variable...
View Full Document

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.

Ask a homework question - tutors are online