Use the applet Hypotheses Test for a Proportion to investigate the effect of the true population proportion p on the probability of a Type I error occurring. For this exercise, use n = 100, and alternative not equal.

a. Set true p = .5 and null p = .5. Run the applet several times and record the proportion of times the null hypothesis is rejected at the .01 level.

b. Clear the applet and repeat part a for true p = .1 and null p = .1. Then repeat one more time for true p = .01 and null p = .01.

c. Based on your results from parts a and b, what can you conclude about the probability of a Type I error occurring as the true population proportion gets closer to 0?