Complete the following problems in a commented R le. Include any output requested as a comment following your code. Save any produced plots in a single PDF le. Problem 1 (25 points): Consider a normally distributed population with mean 26.7 and standard deviation 4.4. Assume that the population mean is unknown to the practitioner, but that she knows the population standard deviation. The practitioner plans to take a random sample from the population to conduct a two-tailed hypothesis test using the one-sample 2- test 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 given 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