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This works exactly if population values have a normal

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Unformatted text preview: is about the Population Mean: Case 1 σ known Case 1: σ known 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 : H0 :µ ≥ µ0 H1 :µ &lt; µ0 A right-tailed test has the H0 and H1 : H0 :µ ≤ µ0 H 1 :µ &gt; µ 0 Utku Suleymanoglu (UMich) Hypothesis Testing 9 / 39 Testing Hypothesis about the Population Mean: Case 1 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 it 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 / 39 Testing Hypothesis about the Population Mean: Case 1 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: H0 :µ ≥ 3 H 1 :µ &lt; 3 This is a left-tailed test. Relevant test statistic for this test (for all Case 1 cases, right or left-tailed or two-tailed) is: z= x − µ0 ¯ 2.5 − 3 = −1.66 √= σ/ n 1.5/5 We will see why we use this. Utku Suleymanoglu (UMich) Hypothesis Testing 11 / 39 Testing Hypothesis about the...
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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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