There's 5 questions in total, thank you!

1. 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 was5069with a standard deviation of4774. Of the 35 four-year colleges surveyed, the average enrollment was5366with a standard deviation of8111. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student'st-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 formoft_dfwheredfis the degrees of freedom. Round your answer to two decimal places.)
2. Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys46entry level mechanical engineers and54entry level electrical engineers. Their mean salaries were$46,300and$46,700, respectively. Their standard deviations were$3410and$4210, respectively. Conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary. Let the subscriptm= mechanicalande= electrical. NOTE: If you are using a Student'st-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.) a. State the distribution to use for the test. (Enter your answer in the formof t_dfwheredfis the degrees of freedom. Round your answer to two decimal places.) b. What is the test statistic? t=___(round your answer to three decimal places.) c. What is thep-value? (Round your answer to four decimal places.)
3. While her husband spent 2 hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of65men,24said they enjoyed the activity.Eightof the24women surveyed claimed to enjoy the activity. Interpret the results of the survey. Conduct a hypothesis test at the 5% level. Let the subscriptm= menandw= women. NOTE: If you are using a Student'st-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. (Round your answers to four decimal places.) P'_mP'_w~ ___ (___, ___)