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A student at a four-year college claims that average 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 average enrollment was 5062 with a standard deviation of 4771. Of the 35 four-year colleges surveyed, the average enrollment was 5566 with a standard deviation of 8141. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's t-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) + Part (b) Part (c) Part (d) Part (e) What is the test statistic? (Round your answer to two decimal places.) ---Select--- O= Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If Ho is false, then there is a chance equal to the p-value that the sample average enrollment at 4-year colleges is at least 504 more than the sample average enrollment at 2-year colleges. O If Ho is true, then there is a chance equal to the p-value that the sample average enrollment at 4-year colleges is at least 504 less than the sample average enrollment at 2-year colleges. O If Ho is false, then there is a chance equal to the p-value that the sample average enrollment at 4-year colleges is at least 504 less than the sample average enrollment at 2-year colleges. If Ho is true, then there is a chance equal to the p-value that the sample average enrollment at 4-year colleges is at least 504 more than the sample average enrollment at 2-year colleges