The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.

1: State the appropriate null and alternative hypothesis.

2: Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the critical value (stated in dollars)?

3: Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis?

4: Referring to your answer in part c, which of the two statistical errors might have been made in tis case explain.