6.36. You can use an applet to repeatedly generate random samples and conduct significance tests, to illustrate their behavior when used for many samples. To try this, go to the significance test for a proportion applet at www.prenhall.com/???. Set the null hypothesis as Hq: tt = 1/3 for a one-sided test {tt > 1/3) with sample size 116, a case Example 6.9 (page 166) on the astrology experiment considered. At the menu, set the true proportion value to 0.33.

(a) Click Simulate and 100 samples of this size will be taken, with the F-value found for each sample. What percentage of the tests were significant at the 0.05 significance level?

(b) To get a feel for what happens "in the long run," do this simulation 50 times, so you will have a total of 5000 samples ofsize 116. What percentage of the samples resulted in a Type 1 error? What percentage would you expect to do so, resulting in a Type I error?

(c) Next, change tt to 0.50, so Hq is actually false. Simulate 5000 samples. What percentage oftimes did you make a Type II error? By Example 6.9 thisshould happen only about 2%

of the time.