4 develop and use a decision rule to make a call

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Unformatted text preview: ce level: α) 3 Calculate a suitable test statistic using available sample statistics to use in conjuction with. . . 4 (Develop and) Use a decision rule to make a call about H0 . (a) Assume the null hypothesis is valid. (b) Figure out the sampling distribution of the sample statistic under the assumption is null hypothesis correct. (c) Figure the distribution of the test statistic under the null. (d) Select a criteria that uses probability distribution of the test statistic to reject or fail to reject the null hypothesis. The criteria uses α as a tolerance level. 5 State your conclusion on the null hypothesis. Utku Suleymanoglu (UMich) Hypothesis Testing 8 / 37 Testing Hypothesis about the Population Mean: σ known σ known: One tailed tests We start with unrealistic case where σ is known. This works exactly if population values have a normal distribution, and approximately if not. One-Tailed Tests A left-tailed test has the H0 and H1 : H 0 : µ ≥ µ0 H1 :µ < µ0 A right-tailed test has the H0 and H1 : H 0 : µ ≤ µ0 H1 :µ > µ0 Utku Suleymanoglu (UMich) Hypothesis Testing 9 / 37 Testing Hypothesis about the Population Mean: σ known Test statistic for tests with known σ ’s will have the test statistic: z= x − µ0 ¯ √ σ/ n Now, we need to come up with a testing criteria. There are two equivalent ways of doing this: p-value approach Critical value (rejection region) approach These are best explained with an example. We will discuss the logic of hypothesis testing with this example. Important Note: We will discuss hypothesis testing regarding µ and p in different scenarios. The first scenario is for µ where σ is known. I will spend an extra amount of time on this case to explain to you the logic of hypothesis testing. This logic carries through everything we are going to do, so I will not repeat at again. Don’t mistake me spending a lot of time on the first case for other cases not being important. Utku Suleymanoglu (UMich) Hypothesis Testing 10 / 37 Testing Hypothesis about the Population Mean: σ known Long Running Example Suppose you think the average lifespan of energy-saving light bulbs is less than 3 years. You collect a sample of 25 newly builty bulbs and measure their lifespan. You get x = 2.5. You (somehow) know standard deviation of their lifespan is σ = 1.5. Then we ¯ have the hypotheses: H 0 :µ ≥ 3 H 1 :µ < 3 This is a left-tailed test. Relevant test statistic for it is: z= Utku Suleymanoglu (UMich) x − µ0 ¯ 2 .5 − 3 √= = −1.66 1.5/5 σ/ n Hypothesis Testing 11 / 37 Testing Hypothesis...
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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.

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