As an incoming Summer Analyst for an investment banking firm, you have been selected to be part of a new project related to employee headcount. Youve been asked to partner with the Human Resources department at the firm to obtain confidential data related to the number of employees in the Market Risk Coverage department. Youve also been tasked to survey each employee of the department. You are required to present the following information to the Firmwide Market Risk Committee:

• What are the overall age descriptive statistics of the Executive Directors within the Market Risk Coverage department?

• Due to a large number of upcoming initiatives, the committee would like to understand how long they can expect the Analysts and Associates to stay within the group before looking for other opportunities. This is a question youve asked each employee through your survey. Provide the 95% confidence interval of the number of years they plan to stay in the group based on your survey results (round to nearest hundredth)

• The committee has come up with a null hypothesis that the department can perform its responsibilities with a headcount of 390 employees. Theyve determined that the departments sigma is 50, and the sample mean will be 395 in the next month. Based on the current sample size of 400, should the committee accept or reject the null hypothesis at a 95% confidence level? Why?

• The committee has been told they must reach a headcount that has a standard deviation of 50 and a sampling error of 5 within the next two years. What is the maximum headcount they can have at a 95% confidence level?

What are the steps to finding these?