ECON206_1011_01_Handout_07

# ECON206_1011_01_Handout_07 - ECON 206 METU- Department of...

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ECON 206 December 06, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: oeruygur@gmail.com 1 LECTURE 07 HYPOTHESIS TESTING - I Outline of today’s lecture: I. Elements of Statistical Test . ............................................................................................... 1 Type I and Type II Errors . ................................................................................................. 4 II. Common Large-Sample Tests . .......................................................................................... 5 III. Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test . ... 12 IV. Another Way to Report the Results of a Statistical Test: p -value . ................................ 18 I. Elements of Statistical Test Usually, the main objective of a statistical test is to test a hypothesis concerning the values of one or more population parameters. We generally have a theory ( a research hypothesis) about the parameter(s) that we wish to support. For example, suppose that a vice president in charge of sales for a large corporation claims that salespeople are averaging no more than 15 sales contacts per week. (He would like to increase this figure.) If we do not believe vice president’s claim, we might seek to support the research hypothesis that vice president's claim is incorrect.

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ECON 206 December 06, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: oeruygur@gmail.com 2 Support for this research hypothesis, also called the alternative hypothesis , is obtained by showing (using the sample data as evidence) that the converse of the alternative hypothesis, called the null hypothesis is false. o In a sense, it is a proof by contradiction . Because we seek support for the alternative hypothesis that vice president's claim is false, our alternative hypothesis is that μ , the mean number of sales contacts per week, is higher than 15. If we can show that the data support rejection of the null hypothesis =15 (the maximum value needed to confirm vice present’s argument) in favor of the alternative hypothesis >15 , we have achieved our research objective. Although it is common to speak of testing a null hypothesis, the research objective usually is to show support for the alternative hypothesis, if such support is warranted . How do we utilize that data to decide between the null hypothesis and the alternative hypothesis? Suppose that n =36 salespeople are randomly selected from the company and Y , the average number sales contracts that salespeople sell in this sample, is recorded. If the average sales contract of the sample is 30 ( Y =30), what would you conclude about vice president's claim? If, in reality, the average sales contract that salespeople sell per week (population parameter, ) is at most 15, it is not impossible to
ECON 206 December 06, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: oeruygur@gmail.com 3 observe Y =30 in a sample of size n =15, but it is highly improbable . It is much more likely that we would observe Y =30 if the alternative hypothesis were true ( μ >15 ). Thus we would reject the null hypothesis ( =15) in favor of the alternative hypothesis ( >15 ). If we observed Y =25 (or any other value of Y very much higher than 15), the same type of reasoning would lead us to the same conclusion.

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## This note was uploaded on 03/22/2012 for the course ECON 106 taught by Professor Kücüksenel during the Spring '12 term at Middle East Technical University.

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ECON206_1011_01_Handout_07 - ECON 206 METU- Department of...

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