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 has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.
a. State the appropriate null and alternative hypotheses.
b. 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)?
c. Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis?
d. Referring to your answer in part c, which of the two statistical errors might have been made in this case? Explain.