# Tutor profile: Isaiah A.

## Questions

### Subject: Microsoft Excel

Describe how you would go about solving a linear optimization problem in Excel using solver

There are 3 components to a linear programming problem: Decision variables - what we're determining the quantities of (changing cells) Objective function - how decision variables affect value we're optimizing (min, max, or value of). Example: we could be maximizing profits, minimizing distances, and more. Constraints - how resources are used by decision variables (how far we can stretch resources). Step 1: In Excel, enter blank cells for decision variables, and write formulas to tie them into the constraints as well as the objective function. Step 2: Open solver. Go to the Data tab -> Data Analysis -> Solver. Step 3: - Point Excel to where objective function's formula is in the "Set Objective" line, then choose Max, Min, or Value of (depending on what the goal is). - Highlight decision variable cells as the Variable Cells - Lastly add each constraint and click solve! (Check to make sure the answer makes sense; it's a good way to catch mistakes).

### Subject: Corporate Finance

Suppose that, on average, stock prices tend to overreact to an unexpected decline in company earnings: the company’s stock drops significantly on the announcement date; then, over the next few weeks, it “bounces back” somewhat, finally ending up lower than the price before the announcement. Describe an investment strategy that “beats the market” in this setting.

Purchase shares immediately after a firm makes a negative announcement then sell a few weeks later. On average, you’ll capture the bounce–back. However, you should note that prices won't fall as far on the announcement if many other investors employ this same strategy. In that case, the excess profits will disappear.

### Subject: Statistics

A poll surveyed the public if they believed that a certain public official possessed honesty and integrity. 518 adults were surveyed and 233, or 0.45 of them answered yes. From this, can we conclude that only a minority (less than half) of the population answered yes?

Step 1. Determine the null and alternative hypotheses. Null hypothesis: There is no clear winning opinion on this issue; the proportions who would answer yes or no are each 0.50. Alternative hypothesis: Fewer than 0.50, or 50%, of the population would answer yes to this question. Step 2. Collect and summarize data into a test statistic. Sample proportion is: 233/518 = 0.45. Standard deviation = sqrt [(0.50 × (1 – 0.50)) / 518] = 0.022. Test statistic: z = (0.45 – 0.50)/0.022 = –2.27 Step 3. Determine the p-value. The alternative hypothesis was one-sided, therefore the p-value would be the portion of the bell-shaped curve to the left of -2.27. Looking on the Unit Normal table, this gives us a value of 0.0116. Step 4. Make a decision. The p-value of 0.0116 is less than 0.05, so we conclude that the proportion of people polled who believed this public official to be honest was significantly less than a majority.