Problem 3 (15 points): Consider the distribution given in Problem 1. Assume that both the population mean and standard deviation are unknown to the practitioner. She plans to take a random sample from the population to conduct a twotailed hypothesis test using the onesample ztest for the mean. For each part, repeat the following steps 10,000 times to conduct a Monte Carlo simulation to estimate the Type I error of the test the practicioner will conduct: i. Draw a random sample of the appropriate size from the population. ii. Determine the test statistic and its associated pvalue. (You should *not* use a testing function.) iii. Record whether the null hypothesis would be rejected or not. (a) Using samples of 15 individuals, determine the proportion of samples that would lead the practitioner to reject the null hypothesis. (b) Using samples of 30 individuals, determine the proportion of samples that would lead the practitioner to reject the null hypothesis. (c) Using samples of 45 individuals, determine the proportion of samples that would lead the practitioner to reject the null hypothesis