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's 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, which has a sample mean of $29,500. If the arbitrator assumes that the blue-collar incomes are distributed with a standard deviation of $8,000, can it be inferred at the 5% significance level that the company president is correct? What is the p-value of the test?
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