Q. Director of a state agency believes that average starting salary for clerical employees in 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 state and found that sample mean is $29,750.

1: State appropriate null and alternative hypothesis.

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

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

4: referring to your answer in part c, which of two statistical errors might have been made in these case> elucidate.