stat104_lecture25v1_1up

# stat104_lecture25v1_1up - Stat 104 Quantitative Methods for...

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Stat 104: Quantitative Methods for Economists Class 25: Hypothesis Testing: Computer Examples 1

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Example The manager of a department store is thinking about establishing a new billing system for the store's credit customers. She determines that the new system will be cost- effective only if the mean monthly account is more an \$170. A random sample of 400 monthly accounts than \$170. A random sample of 400 monthly accounts is drawn, for which the sample mean is \$178, with a sample standard deviation of \$65. Can the manager conclude from this that the new system will be cost-effective? 2
The system will be cost effective if the mean account balance for all customers is greater than \$170. We express this belief as our research hypothesis, that is: H a : μ > 170 (this is what we want to determine) Thus, our null hypothesis becomes: H o : μ = 170 (this specifies a single value for the parameter of interest) 3

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What we want to show: H o : μ = 170 (we’ll assume this is true) H a : μ > 170 We know: n = 400, = 178, and s = 65 What to do next?! 4
To test our hypotheses, we can use two different approaches: The rejection region approach (typically used when computing statistics manually), and The p-value approach (which is generally used with a computer and statistical software). We will explore both in turn… 5

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Rejection region It seems reasonable to reject the null hypothesis in favor of the alternative if the value of the sample mean is large relative to 170. c 6
Rejection Region s From previous classes we know to reject the null hypothesis if 65 1.64 170 1.64 175.34 400 o s x n μ + = + = s Or, equivalently, s Conclusion? It is cost effective to install the new billing system 7 178 170 2.46 1.64 / 65 / 400 o stat x z s n - - = = = >

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The Big Picture =175.34 =178 H 0 : = 170 H 1 : > 170 Reject H 0 in favor of 8
The Big Picture Again .05 0 t = 2.46 H 0 : = 170 H 1 : > 170 Reject H 0 in favor of 1.64 9

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P-Value of a Test The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true. In the case of our department store example,
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## This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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stat104_lecture25v1_1up - Stat 104 Quantitative Methods for...

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