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 5,068 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 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) State the distribution to use for the test. (Enter your answer in the form z or toy where of is the degrees of freedom. Round your answer to two decimal places.) Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) t v v = 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 true, then there is a chance equal to the p-value that the sample mean enrollment at 4-year colleges is at least 398 more than the sample mean enrollment at 2-year colleges. If Ho is true, then there is a chance equal to the p-value that the sample mean enrollment at 4-year colleges is at least 398 less than the sample mean enrollment at 2-year colleges. If Ho is false, then there is a chance equal to the p-value that the sample mean enrollment at 4-year colleges is at least 398 more than the sample mean enrollment at 2-year colleges. If Ho is false, then there is a chance equal to the p-value that the sample mean enrollment at 4-year colleges is at least 398 less than the sample mean enrollment at 2-year colleges. Correct! A p-value is the probability that an outcome of the data will happen purely by chance when Ho is true. Part (9) Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) a = (ii) Decision: O reject the null hypothesis do not reject the null hypothesis (iii) Reason for decision: Since p-value > ox, we do not reject the null hypothesis. Since p-value ox, we reject the null hypothesis. O Since p-value