Arecruiting office believes that the mean entry-level salary for data scientists is higher than the mean entry-level salary for software engineers. the recruiting office randomly surveys 30 entry level data scientists and 40 entry level software engineers. their mean salaries were $82,500 and $79,500, respectively. their standard deviations were $4,750 and $3,250, respectively. perform a hypothesis test at the a = 0.05 significance level to determine whether the belief of the recruiting office is supported by the evidence and answer the following questions: a. suppose that uy is the mean entry-level salary for data scientists and uz is the mean entry-level salary for software engineers. what are the null and alternative hypotheses of the test? b. which distribution do you use to perform the test (normal or student's t)? c. is the test right-, left., or two-tailed? d. calculate the test statistic and the p-value. e. what conclusion do you make from the test?