Problem 3: GMU Shuttle Service GMU officials are trying to determine if they are using the correct number of campus shuttles for the number of students who use them. If the proportion of students who use the shuttles is significantly different from 0.28, the officials believe they will have to either remove or add a shuttle to the eet. In a random sample of 444 people taken from the population of all individuals associated with GMU (including faculty, staff, and students) it was discovered that 123 of these individuals use the shuttle. a) Check the three conditions of the Central Limit Theorem that allow you to use the one- proportion confidence interval using one complete sentence for each condition. Show work for the numerical calculation. b) Construct a 99% confidence interval to estimate the population proportion of these individuals who use the shuttle system. Calculate this \"by hand\" using the formula and showing your work (please type your work, no images accepted here). Round your confidence limits to four decimals. c) Verify your result in part (a) using Stat [l Proportions Stats |] One Sample I] With Summary. Copy and paste your StatCrunch result in your document as well. d) Using on = 0.01, is there sufficient evidence to conclude that the proportion of students who use GMU shuttles is different from 0.28? Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. i. Define the population parameter in one sentence. ii. State the null and alternative hypotheses using correct notation. iii. State the significance level for this problem. iv. Calculate the test statistic \"by-hand.\" Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round during the calculation. Then, round the test statistic to two decimal places after you complete the calculation