Applet Exercise Refer to Exercise 10.10. Click the button

Chapter 10, Problem 15E

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Problem 15E

Applet Exercise Refer to Exercise 10.10. Click the button “Clear Summary” to delete the results of any previous simulations. Change the sample size for each simulation to n = 30 and set up the applet to simulate testing H0 : p = .4 versus Ha : p > .4 at the .05 level of significance.

a Click the button “Clear Summary” to erase the results or any previous simulations. Set the real value of p to .4 and implement at least 200 simulations. What is the percentage simulated tests that result in rejecting the null hypothesis? Does the test work as you expected?

b Leave all settings as they were in part (a) but change the real value of p to .5. Simulate at least 200 tests. Repeat when the real value of p is .6 and .7. Click the button “Show Summary.” What do you observe about the rejection rate as the true value of p gets further from .4 and closer to 1? Does the pattern that you observe match your impression of how a good test should perform?

Reference

Applet Exercise Refer to Exercise 10.9. Click the button “Clear Summary” to delete the results of any previous simulations. Change the sample size for each simulation to n = 30 and leave the null and alternative hypotheses at their default settings H0 : p = .5, Ha : p 7= .5.

a Leave the true value of p at its default setting p = .5.With this scenario, what is an error? Simulate at least 200 tests. What proportion of the tests resulted in rejecting H0? What do you notice about the heights of the boxes above “Reject” and “Error” in the bottom right-hand graph? Why?

b Leave all settings unchanged except change the true value of p to .6.With this modification, what is an error? Simulate at least 200 tests. What proportion of the tests resulted in rejecting H0? What do you notice about the heights of the boxes above “Reject” and “Error” in the bottom right-hand graph? Why?

c Leave all settings from part (b) unchanged except change the true value of p to .7. Simulate at least 200 tests. Repeat, setting the true value of p to .8. Click the button “Show Summary.” As the true value of p moves further from .5 and closer to 1, what do you observe about the proportion of simulations that lead to rejection of H0? What would you expect to observe if a set of simulations was conducted when the true value of p is .9?

d What would you expect to observe if simulations were repeated when the real value of p is .4, .3, and .2? Try it.