The director of a state agency believes that the average starting salary for clerical employees in the state is less than $27,000 per year. To test her hypothesis, she collected a simple random sample of 100 starting salaries for clerical employees across the state and found that the sample mean is $26,550. She assumes that the population standard deviation is known to be $3,000 and the significance level for the test is 0.05. State the appropriate null and alternative hypotheses. Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis? Which of the two statistical errors might have been made in this case? Explain.