Applet Exercise Refer to Exercise 10.9. Set up the applet to test H0 : p = .1versus Ha

Chapter 10, Problem 10.14

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Applet Exercise Refer to Exercise 10.9. Set up the applet to test H0 : p = .1versus Ha : p < .1 by clicking the radio button Lower in the line labeled Tail and adjusting the hypothesized value to .1. Set the true value of p = .1, n = 5, and = .20. a Click the button Draw Sample until you obtain a sample with zero successes. What is the value of z? What is the smallest possible value for z? Is it possible that you will get a sample so that the value of z falls in the rejection region? What does this imply about the probability that the large sample test procedure will reject the null hypothesis? Does this result invalidate the use of large sample tests for a proportion? b Will the test from part (a) reject the true null approximately 20% of the time if we use n = 10? Try it by simulating at least 100 tests. What proportion of the simulations result in rejection of the null hypothesis? c Look through the values of p in the table under the normal curve and identify the value of p for which the null is rejected. Use the tables in the appendix to compute the probability of observing this value when n = 10 and p = .1. Is this value close to .2? d Is n = 100 large enough so that the simulated proportion of rejects is close to .2? Simulate at least 100 tests and give your answer based on the simulation.