# X press the scale to fit button to redraw and scale

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x Press the Scale To Fit button to redraw and scale the curve. x Check the box next to the first < sign to activate that row. x Specify the value of interest in the Probability box. Press Enter/Return . Step 2: Determine the probability under the alternative of a result in the rejection region (d) Assume the probability of a correct identification is S = 0.30. Calculate the probability of the result you found in (c) with a sample size of n = 329. [ Hint : Use your technology “in the other direction”] [Include a sketch of the relevant distribution.] Interpret your result in context.
Chance/Rossman, 2016 ISCAM III Exploration 89 Many software packages will calculate power for you, especially with the normal approximation to the binomial. Technology Detour Calculating Power (Normal) In R: The iscamnormpower function uses the following inputs x LOS = the desired level of significance ( D ) x n = the sample size (number of trials) x prob1 = the process probability ( S ) under the null hypothesis x alternative = “less”, “greater”, or “two.sided” x prob2 = the alternative probability of success For example: > iscamnormpower(LOS=.05, n=20, prob1=.25, alternative = "greater", prob2=0.333) should reveal both distributions and report the rejection region to achieve the level of significance, the observed level of significance, and the power. In Minitab x Choose Stat > Power and Sample Size > 1 Proportion x Specify the sample size(s), specify alternative values in the first two boxes. x Specify the hypothesized probability in the last box. x Under Options specify the direction of the alternative and the level of significance. x Keep the Distribution pull-down menu set to Normal and specify the values for the mean and standard deviation. x Press the Shaded Area tab. Define the Shaded Area by Probability , specify the tail direction, and enter the observation value of interest. Press OK . Power Simulation Applet x There is a Normal Approximation check box. In fact, the most common application is to specify the desired power and solve for the necessary sample size before conducting the study to determine how many observational units you should recruit. (e) If your technology allows, see how many sessions would be needed in the ESP study to have at least an 80% chance of rejecting the null hypothesis if the actual probability of success is S = 0.30. (f) How will your answer change if the actual probability of success is S = 0.35?
Chance/Rossman, 2016 ISCAM III Exploration 90 Practice Problem 1.11B Suppose that you want to re-conduct the kissing study in a large city with a sample of 100 kissing couples. You want to test the null hypothesis H 0 : S = 0.667 against a one-sided alternative H a : S < 0.667 using a significance level of D = 0.05, and you are concerned about the power of your test when S = 0.5. Consider the following graph: (a) Which region(s) represents the probability of making a Type I error?