Math 246 Project 9 Sample KEY (1)

# Math 246 Project 9 Sample KEY (1) - Note that decision...

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KEY Project 9 You will be graded on completeness. Power is the probability that we reject the null hypothesis when the alternative hypothesis is assumed to be true. We will construct a Power Curve. Null: = 105 Alternative: 105 This is a two tailed test. We need to have two areas of rejecting the =105. A simple random sample of size 35 is obtained from a population with =12. If the researcher decides to test this hypothesis at the = 0.10 then compute the power and draw the power curve. State the necessary assumptions: We will assume that the sampling distribution of the sample mean is approximately Normally distributed with μx approaches the = 105 And the standard error σx approaches σ/√n = 12/√35 = 2.03 Construct the decision rule using the classical method. There are two rejection regions that are determined by: P( x < Decision maker 1) = α/2 = 0.05, and P( x > Decision maker 2) = α/2 = 0.05.

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Unformatted text preview: Note that decision maker 1 is the 5 th percentile; so, using the TI 83/84 invNormal(0.05,105,2.03) the decision maker 1is 101.66. The decision maker 2 is the 95 th percentile; so, using TI 83/84 invNormal(0.95,105,2.03) the decision maker 2 is 108.34. Decision Rule (classical approach): If the sample mean is less than 101.66 OR the sample is greater than 108.34, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. POWER: Using TI: normcdf(-∞, 101.66,E , 1 . )+ ( . , 2 03 normcdf 108 34 ∞ , , 1 . ) 2 03 Possible values of (assuming the alternative is true) Power 111 .90544 110 .7940 109 .6284 107 .2593 106 .1410 104 .1410 103 .2593 99 .90544 98 .9646 97 .9893 Construct the Power Curve: 112.5 110.0 107.5 105.0 102.5 100.0 97.5 95.0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 MEAN POWER Scatterplot of POWER vs MEAN...
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Math 246 Project 9 Sample KEY (1) - Note that decision...

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