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 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Of the 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Test the student's claim at the 0.10 significance level. a) The null and alternative hypothesis would be: O Ho: PF = HT H₁: HP PT Ho: PF PT H₁: PF PT = HT O Ho: PF H₁:μp PT O Ho: PF = PT H₁: PF > PT b) Determine the test statistic. Round to two decimals. t c) Find the p-value and round to 4 decimals. = P d) Make a decision. O Reject the null hypothesis Fail to reject the null hypothesis e) Write the conclusion. O There is sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. O There is not sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. -

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