9
You KEY
Project 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: Alternative: =105. A simple random sample of size 35 is obtained from a population with =12. = 105 105 This is a two tailed test. We need to have two areas of rejecting the
If the researcher decides to test this hypothesis at the power curve. State the necessary assumptions:
= 0.10 then compute the power and draw the
We will assume that the sampling distribution of the sample mean is approximately Normally distributed with x approaches the = 105
And the standard error
x
approaches /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) = /2 = 0.05, P(x> and Decision maker 2) = /2 = 0.05. Note that decision maker 1 is the 5th 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 95th 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,E1,2.03)+normcdf(108.34,, Possible values of (assuming the alternative is true) 111 110 109 107 106 104 103 99 98 97 Power .90544 .7940 .6284 .2593 .1410 .1410 .2593 .90544 .9646 .9893
1,2.03)
Construct the Power Curve:
Scatterplot of POWER vs MEAN
1.0 0.9 0.8 0.7 POWER 0.6 0.5 0.4 0.3 0.2 0.1 95.0 97.5 100.0 102.5 105.0 MEAN 107.5 110.0 112.5