Health policy analysts examining the potential impact of staffing increases on total hospital costs have assumed that the general population of female administrators make on average $85,000 per year with a standard deviation of $1,200. Critics of their methodology challenge this assumption, explaining that if the true mean annual salary is off by $500 or more, the key conclusions of the health policy analysis may be misleading. They plan to conduct survey of randomly selected female administers to test the mean salary assumption used by the policy analysts.

• 4a. How large of a sample is needed to detect a $500 difference with 80% power at the two-sided 5% level of significance? Show your STATA command or hand calculations.
• 4b. Would you need a larger or smaller sample to detect a $300 difference with 80% power at the two-sided 5% level of significance? Justify your answer by providing an appropriate calculation of sample size.