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: OH:LF=UT Η : με > με O Ho PF PT H₁: PF PT O Ho μFμT Η : με 7 μπ = O Ho PF PT H₁ PF PT O Ho μFμT Η : με < μτ = 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 Fail to reject the null hypothesis O Reject the null hypothesis e) Write the conclusion. O There is not sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. There is sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. The average student loan debt is reported to be $25,235. A student belives that the student loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean to be $27,524 and the standard devition to be $6000. Is there sufficient evidence to support the student' claim at a 5% significance level? a) Determine the null and alternative hypotheses. Ho: Ha: Select an answer (Put in the correct symbol and value) b) Determine the test statistic. Round to two decimals. t= c) Find the p-value. Round to 4 decimals. P-value = d) Make a decision. O Fail to reject the null hypothesis O Reject the null hypothesis e) Write the conclusion. O There is not sufficient evidence to support the claim that student loan debt is higher than $25,235. O There is sufficient evidence to support the claim that student loan debt is higher than $25,235.