Let denote the proportion of voters in a certain state who favor a particular proposed constitutional amendment Consider testing H 0 5 versus H a 5 at significance level 05 based on a sample of size n 50 a Suppose that H 0 is in fact true Use Appendix Table 1 (our table of random numbers) to simula...

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Let denote the proportion of voters in a certain state who favor a particular proposed constitutional

Question:

Let π denote the proportion of voters in a certain state who favor a particular proposed constitutional amendment. Consider testing H₀: π = .5 versus H_a: π > .5 at significance level .05 based on a sample of size n = 50.

a. Suppose that H₀ is in fact true. Use Appendix Table 1 (our table of random numbers) to simulate selecting a sample, and use the resulting data to carry out the test.

b. If you repeated Part (a) a total of 100 times (a simulation consisting of 100 replications), how many times would you expect H₀ to be rejected?

c. Now suppose that π = .6, which implies that H₀ is false. Again, use Appendix Table 1 to simulate selecting a sample, and carry out the test. If you repeated this a total of 100 times, would you expect H₀ to be rejected more frequently than when H₀ is true?

Data from Appendix table 1 Random Numbers