Average entw level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same.'r A recruiting office thinks that the average mechanical engineering salary is actually lower than the average electrical engineering salary. The recruiting office randomly surveys 50 entry level mechanical engineers and 56 entry level electrical engineers. Their average salaries were $46,200 and $46,700, respectively. Their standard deviations were $3420 and $4240, respectively. Conduct a hypothesis test at the 5% level to determine if you agree that the average entry level mechanical engineering salary is lower than the average 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.) What is the p-value? (Round your answer to four decimal places.)