Management claims that the mean income for all senior-level assembly-line workers in a large company equals $500 per week. An employee decides to test this claim, believing that it is actually less than $500. For a random sample of nine employees, the incomes are
430, 450, 450, 440, 460, 420, 430, 450, 440.
Conduct a significance test of whether the population mean income equals $500 per week against the alternative that it is less. Include all assumptions, the hypotheses, test statistic, P-value, and interpret the result in context.