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Supplement_6

Supplement_6 - HYPOTHESIS TESTING HYPOTHESIS TESTING...

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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ HYPOTHESIS TESTING ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ HYPOTHESIS TESTING Documents prepared for use in course C22.0103.001 , New York University, Stern School of Business The logic of hypothesis testing, as compared to jury trials page 3 This simple layout shows an excellent correspondence between hypothesis testing and jury decision-making. t test examples page 4 Here are some examples of the very widely used t test. One-sided tests page 8 We need to be very careful in using one-sided tests. Here are some serious thoughts and some tough examples. An example of a one-sided testing environment page 1 2 Most of the time we prefer two-sided tests, but there are some clear situations calling for one-sided investigations. 1
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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ HYPOTHESIS TESTING ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ What are the uses for hypothesis tests? page 13 This discusses the situations in which we use hypothesis testing. Included also is a serious discussion of error rates and power curves. Gary Simon, 2003 Revised by Avi Giloni 2005 Cover photo: Yasgur farm, Woodstock, New York 2
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| | | | | HYPOTHESIS TESTING COMPARED TO JURY TRIALS | | | | | COMPARISONS BETWEEN HYPOTHESIS TESTS AND JURY DECISION-MAKING General Specific Example Criminal Trial Null Hypothesis H 0 : µ = 28 (where µ is the unknown mean of some population) Defendant is innocent Alternative Hypothesis H 1 : µ 28 Defendant is guilty Data Sample x x x n 1 2 , ,..., Testimony Decision mechanism t test Jury deliberation Accept null hypothesis H 0 Decide µ = 28 Acquittal (decide innocent or insufficient evidence to convict) Reject null hypothesis H 0 Decide µ 28 Convict (decide that defendant is guilty) Type I error Decide µ 28 when H 0 holds Decide guilty when defendant is innocent Type II error Decide µ = 28 when H 0 is wrong Decide innocent when defendant is guilty 3
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¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ t TEST EXAMPLES ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ EXAMPLE 1: A health-care actuary has been investigating the cost of maintaining the cancer patients within its plan. These people have typically been running up costs at the rate of $1,240 per month. A sample of 15 cases for November (the first 15 for which complete records were available) and an average cost of $1,080, with a standard deviation of $180. Is there any evidence of a significant change? SOLUTION: Let’s examine the steps to a standard solution. Step 1: The hypothesis statement is H 0 : µ = $1,240 versus H 1 : µ $1,240. Observe that µ represents the true-but-unknown mean for November. The comparison value $1,240 is the known traditional value to which you want to compare µ . Do not be tempted into using H 1 : µ < $1,240. The value in the data should not prejudicially influence your choice of H 1 . Also, you should not attempt to second-guess the researcher’s motives; that is, you shouldn’t try to create a story that suggests that the researcher was looking for smaller costs. In general, you’d prefer to stay away from one-sided alternative hypotheses.
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