1. Suppose we want to test Ho: p = 0.5 vs. Ha:p > 0.5 using a sample proportion of 520 out of 1000, or 0.52. a. Find the p-value using a randomization distribution in StatKey. b. What is the standard error from the randomization distribution in part a? Now model the randomization distribution with a normal distribution with mean 0.5 from the null hypothesis and standard deviation equal to this standard error that you wrote above. Find the p-value by finding the area to the right of p = 0.52 in this standard normal distribution. (In Statkey, go to Theoretical Distributions -> Normal, edit the parameters, choose the appropriate tail(s) to match the alternative hypothesis, and edit the cutoff value.) What is the p-value in this case? c. Find the standardized test statistic. Now, find the p-value by finding the area beyond this standardized test statistic in the standard normal distribution. You may use the standard normal distribution in Statkey or a table of standard normal probabilities to find the area/p-value. In either case, sketch a graph of the standard normal distribution and shade the area that you are finding below. Also, clearly indicate the area/p-value. d. Compare the three p-values found above. What do you notice