Use the applet entitled Hypotheses Test for a Proportion to investigate the relationships between the probabilities of Type I and Type II errors occurring at levels .05 and .01. For this exercise, use n = 100, true p = 0.5, and alternative not equal.
a. Set null p = .5. What happens to the proportion of times the null hypothesis is rejected at the .05 level and at the .01 level as the applet is run more and more times? What type of error has occurred when the null hypothesis is rejected in this situation? Based on your results, is this type of error more likely to occur at level .05 or at level .01? Explain.
b. Set null p = .6. What happens to the proportion of times the null hypothesis is not rejected at the .05 level and at the .01 level as the applet is run more and more times? What type of error has occurred when the null hypothesis is not rejected in this situation? Based on your results, is this type of error more likely to occur at level .05 or at level .01? Explain.
c. Use your results from parts a and b to make a general statement about the probabilities of Type I and Type II errors at levels .05 and .01.
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