In the midst of labor$$management negotiations, the president of a company argues that the

company$$s blue$-$collar workers, who are paid an average of $$50,000$ per year, are well paid

because the mean annual income of all blue$-$collar workers in the country is less than

$$50,000.$ That figure is disputed by the union, which does not believe that the mean blue$-$collar

income is less than $$50,000.$ To test the company president$$s belief, an arbitrator draws a

random sample of $350$ blue$-$collar workers from across the country and asks each to report

their annual income. If the arbitrator assumes that the blue$-$collar incomes are normally

distributed with a standard deviation of $$15,000,$ can it be inferred at the $5\%$ significance level

that the company president is correct? sample mean is $48415$