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 surveys 42 entry level mechanical engineers and 58 entry level electrical engineers. Their mean salaries were $46,200 and $46,800, respectively. Their standard deviations were $3410 and $4240, 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 subscript m = mechanical and e = electrical. 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.) (1) 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.)
(2) 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.)
(3) What is the p-value? (Round your answer to four decimal places.)
(4) write an appropriate conclusion.