In economics two tailed tests are performed a lot to

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Unformatted text preview: to choose one over the others. But we usually don’t use α = 0.2. And nevery a high α like α = 0.8. The nice thing about providing p-values is that you allow the readers to pick their own α’s and arrive at their own conclusions quickly. Utku Suleymanoglu (UMich) Hypothesis Testing 21 / 39 What determines test results? σ is known: Two Tailed Tests Now we will discuss a slightly different type of test. The difference is in the null and alternative hypothesis tests: H0 :µ = µ0 H1 :µ = µ0 These type of tests judge the claim that unknown population parameter is exactly equal to some number. In economics, two-tailed tests are performed a lot to test things like: Whether a production technology have constant returns to scale. (population parameter=1) Whether a job training program has any effect on wages whatsoever. (population parameter=0) We will come back to the latter one again when we do regression analysis. Utku Suleymanoglu (UMich) Hypothesis Testing 22 / 39 What determines test results? Example Test procedure is very similar to the one-tailed tests with a few but important differences. Suppose with your lightbulb sample (remember x = 2.5, n = 25 and σ = 1.5.) Now suppose that ¯ there is a claim that says the mean life expectancy of lightbulbs is 2.6 years: H0 :µ = 2.6 H1 :µ = 2.6 The test statistic is going to be identical with one-tailed tests: z= 2.5 − 2.6 x − µ0 ¯ = −0.33 √= σ/ n 0.3 The test statistic calculates the relative position of 2.5 with respect to hypothesized value for µ: 2.6. You can see it is fairly close as measured by z = −0.33. Given that normal distribution is ¯ bell-shaped, we know x = 2.5 draw from the distribution of X is quite probable if µ = 2.6, so we ¯ should not reject the H0 . Key thing: Because of the equality in the null, what we consider unlikely (under the assumption that the null hypothesis is true) can be on either tail. We will build our rejection regions on both tails. Utku Suleymanoglu (UMich) Hypothesis Testing 23 /...
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