Let p be the probability that your printer operates successfully for a job, and suppose that the operation is independent across jobs. You have printed 20 jobs in a day, and all are successful. a. You want to find out how reliable your printer is. The point estimate for the reliability p is just 1, and the standard error is 0. We know a printer cannot always work, so this approach clearly fails. Instead, test the hypothesis Ho :p = Po HA :p > Po VS = 0.92. First write down the formula for calculating at the 0.05 significance level, where po the p-value. Then use pbinom to find the p-value for this problem. b. Create a confidence interval for the success probability p by inverting the hypothesis test (namely, the confidence interval contains all po so that you do not reject Ho; for code implementation, discretize the candidate po E [0, 1]). This interval estimate is a more reasonable assessment of the reliablity than the point estimate. c. Use binom.test to verify your result in the last part.