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 $30,000 per year, are well paid because the mean annual income of all blue-collar workers in the country is less than $30,000. That figure is disputed by the union, which does not believe that the mean blue-collar income is less than $30,000.

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 his or her annual income. If the arbitrator assumes that the blue-collar incomes are normally distributed with a standard deviation of $8,000, can it be inferred at the 5% significance level that the company president is correct?