This works exactly if population values have a normal

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: 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 < µ0 A right-tailed test has the H0 and H1 : H0 :µ ≤ µ0 H 1 :µ > 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 < 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...
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