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Unformatted text preview: Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 9 22 Week 9 topics l Calculating probability of type 2 errors l Power of test l Hypothesis testing & confidence intervals for the mean when population variance is unknown l t distribution l Sampling distribution of sampling proportion l Hypothesis testing & confidence intervals for the population proportion l Key references l Keller 11.3-11.4, 12.1, 9.2 pp 309-14, 12.3 33 Type I errors in hypothesis testing l Type I errors occur when we reject a true null hypothesis l Denote P (Type I error) = P (Reject H 0| H 0 true) = l Analyst specifies l Typical values chosen for in applications are 0.10, 0.05 or 0.01 l Value of is called the significance level of the test Type II errors in hypothesis testing l Type II errors occur when we dont reject a false null hypothesis l Denote P (Type II error) = l For given there will be a range of values (depending on the true alternative) l Can be calculated for all values under alternative P (Do not reject H 0 | H 0 not correct) = l Changing for given fixed alternative changes l There is a tradeoff between the 2 types of errors 44 55 Calculating probability of Type II errors l Recall McDonalds example l H 0: = 0.25, H 1: < 0.25 l With n = 25, = 0.05, = 0.05 previously found a decision rule (DR) of rejecting H 0 if sample mean < 0.2336 l Suppose that McDonalds only puts 0.24 pounds in their quarter pounder. Will we detect this? 66 Power of a test l Defined as the probability of correctly rejecting a false null hypothesis l P (Do not reject H 0| H 0 not correct) = l P (Reject H 0| H 0 not correct) = Power = 1- l Keller p. 370, (Fig. 11.10) l H 0: = 170; H 1: > 170 l n = 400, = 0.01, = 65 l DR: reject H 0 if sample mean > 177.57 l Power if = 180? 77 Power of a test l What happens to power if increase to 0.05? l What happens to power if increase n to 1000? Power of a test... l Summary l H 0: = 170; H 1: = 180 l If = 0.01, then = 0.2266 ( Power = 0.7734) when n= 400 l If = 0.05, then = 0.0764 ( Power = 0.9236) when n= 400 l If = 0.05, then 0.0000 ( Power 1) when n= 1000 l With a different alternative e.g. With a different alternative e....
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This note was uploaded on 07/28/2011 for the course ECON 1203 taught by Professor Denzilgfiebig during the Three '11 term at University of New South Wales.

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