Applet Exercise In Exercise 10.9(h), you observed that when the null hypothesis is true

Chapter 10, Problem 10.11

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Applet Exercise In Exercise 10.9(h), you observed that when the null hypothesis is true, for all sample sizes the proportion of the time H0 is rejected is approximately equal to the probability of a type I error. If we test H0 : p = .5, Ha : p = .5, what happens to the value of when the sample size increases? Set the real value of p to .6 and keep the rest of the settings at their default values ( = .05, n = 15). a In the scenario to be simulated, what is the only kind of error that can be made? b Click the button Clear Summary. Conduct at least 200 simulations. What proportion of the simulations resulted in type II errors (hover the pointer over the box about Error in the lower right portion of the display)? How is the proportion of type II errors related to the proportion of times that H0 is rejected? c Change n, the number of trials used for each simulated test, to 30 and leave all other settings unchanged. Simulate at least 200 tests. Repeat for n = 50 and n = 100. Click the button Show Summary. How do the values of (.6), the probability of a type II error when p = .6, change as the sample size increases? d Leave the window with the summary information open and continue with Exercise 10.12.