A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480 were delivered on time. a) Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service. b) The manager of the Postal Services claims that 98 percent of their mail are delivered on time. He wants to test at the 1% significance level to determine whether the true proportion is less than 98 percent. i. Give the null and alternative hypothesis of this test. ii. Determine the critical value(s) of this test. iii. Compute the value of the test statistic. iv. State the decision rule. v. Give your decision based on the available sample evidence. vi. Hence, state your conclusion.