2. An independent team of programmers designs 25 specific tasks to test the algorithms discussed in Question 1. The aim is to prove that the new proposal is faster than the current version. For this, they test the current and new implementation in each condition, storing the times in minutes in q2. c and q2.n, respectively. The times are stored in order, i.e., the values in the first position represent the times obtained from task 1, in the second position the ones obtained in task 2, and so on. (a) Calculate the means and standard deviations. (b) Define the null and alternative hypotheses. Define the parameter(s). (c) Does the data support the claim that the new algorithm is faster than the current one using a significance level of 0.05? Perform a hypothesis test, making the corresponding assumptions. Interpret the results in such a way that anybody can understand.# INSTRUCTIONS TO GENERATE THE DATA IN 2 STEPS # STEP 1: INSERT YOUR ID NUMBER ID = 123; # REPLACE 123 with your ID number # STEP 2: Select from Line 1 to line 54 and run the code (at once) ############################### ### DO NOT EDIT THIS R CODE ### ############################### f = function(x, m, s) { return(- (x-m)42 / (2*542)); mcmc = function(n , m, s){| out = rep (NA, n) ; XO = m; like = f(x0, m, s); for (i in 1:n) { for (j in 1:50) { aux = runif (1, x0 - s, x0 + s); like0 = f(aux, m, s); alpha = like0 - like; if (-rexp(1)