rcode please

3. (20 ) Let X be a random variable with mean . When X has normal distribution or the sample size is sufficiently large, the t-test is used to test the hypotheses Ho: p= HO VS Ha : > Po for some hypothesised value po. The t-test is implemented in R using the t. test command. If neither X is normally distributed nor the sample size is sufficiently large, a nonparametric alternative to the t-test is the Wilcoxon test which is implemented in R using the command wilcox. test. Conduct a small Monte Carlo study to compare the performance of the two tests when X has (i) normal distribution N(#, 1) and (ii) double exponential distribution (location = p and rate = 1). You can sample from the double exponential distribution using the command rdexp from the nimble package. For each distribution, use three sample sizes n = 15, 25, 50. Use o = 0.05 for both tests, and set /o = 0. a. For each sample size and each distribution, compute the observed significance level of the t-test and the wilcoxon test by sampling from each distribution under the null hypothesis Ho. Use m = 10, 000 Monte Carlo samples. b. For each sample size and each distribution, compute the power of the t-test and the wilcoxon test by sampling from each distribution under the alternative hypothesis H. with #1 = seq (0, 1, 0.05). Use m = 10, 000 Monte Carlo samples. For each sample size and distribution, plot the power curves for the two tests in the same plot using different colors for the curves