In section 1.4 the times to first exit-site infection (in months) of patients with renal insufficiency were reported. In the study 43 patients had a surgically placed catheter (group 1) and 76 patients had a percutaneous placement for their catheter (Group 0) (a) For both groups fit a Weibull model to the data. Find the maximum likelihood estimates of lambda and alpha, and their standard errors. (b) For both groups test the hypothesis that the shape parameter alpha, is equal to 1 using the likelihood ratio test and the Wald test. (c) Fit a weibull regression model to this data with a single covariate, Z, that indicates group membership. Test the hypothesis of no effect of catheter placement on the time to exit site infection. Find point estimates and 95% confidence intervals