A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 two-year colleges surveyed, the mean enrollment was 5,065 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's -distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though) Part (a) State the null hypothesis OH Hay Hap O Hoj Pay CPAT O Ho Hay Hay Part() State the alternative hypothesis OH May May OHj Hay Hay OH, P- -Per OH May Pay Part() In words, state what your random variable XX represents. represents the mean enrollment in two-year colleges and four-year colleges OXX represents the mean difference in enrollment of two-year colleges and four-year colleges OXX represents the difference in the mean enrollment of beo-year colleges and four-year colleges represents the difference in enrollment of two-year colleges and four-year colleges - Comes The investigation is to determine if the mean enement in four-year colleges is higher than i difference in the mean ment Part (d) State the distribution to use for the best. (Enter your answer in the form or where of is the degrees of freedom. Round your answer to two decimal places) Part() What is the test statistic? If using the distribution round your answer to two decimal places and if using the distribution round your answer to three decimal places)