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A student at a four-year college claims that average enrollment at four-year colleges is higher than...

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 5066 with a standard deviation of 4775. Of the 35 four-year colleges surveyed, the average enrollment was 5516 with a standard deviation of 8131. 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.) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.) Part (e) What is the test statistic? (Round your answer to two decimal places.) t = Part (f) What is the p-value? (Round your answer to four decimal places.)

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