Each sheet contains a yellow cell for each answer. You may use blank areas in the spreadsheet for intermediate steps. Put your final answer in the yellow cell. For numeric answers, do not "hard code" your answers. Enter the formula that yields the answer rather than typing the numeric answer. Your company sells detergent. You are test marketing two types of branding: flashy (which includes bold colors, a contoured package, and large lettering) and subdued (which includes muted pastel colors, a square package, and normal lettering). For 90 days, you sell the product with flashy branding in test market A and the product with subdued branding in test market B. Prior research has verified that the two test markets are identical in every meaningful way (consumers in the two test markets have similar tastes, similar incomes, similar demographics, etc.). The data below show unit sales in each market. You charged the same price per unit in both test markets. The flashy branding costs $6 million annually. The subdued branding costs $5 million annually. The unit contribution (price of the product less the cost of labor, materials, and shipping, on a per-unit basis) is $10. Over the course of the 90-day trial, which branding generated the greater contribution (unit contribution x units sold)? If future sales were identical to what you observed during the 90-day test, which branding would be more profitable? How do you know this? Because sales will fluctuate randomly for reasons that have nothing to do with branding, future sales will not be identical to what you observed over the 90-day test. What is the probability that the difference you observed in the unit sales during the test period was, in fact, simply due to random chance? Based on these results, would you be comfortable assuring senior management that the flashy branding will increase sales enough to justify the additional $1 million cost? Explain. Sales per Day Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Day 11 Day 12 Day 13 Day 14 Day 15 Day 16 Day 17 Day 18 Day 19 Day 20 Day 21 Day 22 Day 23 Day 24 Day 25 Day 26 Day 27 Day 28 Day 29 Day 30 Day 31 Day 32 Day 33 Day 34 Day 35 Day 36 Day 37 Day 38 Day 39 Day 40 Day 41 Day 42 Day 43 Day 44 Day 45 Day 46 Day 47 Day 48 Day 49 Day 50 Day 51 Day 52 Day 53 Day 54 Day 55 Day 56 Unit Sales in Test Market A (flashy branding) 2999 2244 3038 1609 2707 2227 2468 2537 2195 2302 2403 2363 2895 2241 1303 2344 2609 1899 2250 2263 2512 3000 2135 1470 1956 2432 1508 1780 2008 3311 1668 1707 1846 1657 1474 2182 1726 2518 1630 1865 973 2618 1791 2235 2099 2248 2134 2524 2567 2066 2264 2130 1508 2563 1708 2558 Unit Sales in Test Market B (subdued branding) 2141 2703 1803 1566 1677 1911 1170 1654 1645 2226 1900 1917 1900 2473 2005 2588 2110 1844 1986 2463 1699 1691 2069 2256 921 2232 1023 2234 2567 2221 3160 1910 2951 2048 1864 2514 2384 2164 2917 2499 2334 2430 2998 1415 2344 1880 2122 1577 1708 2509 2262 1405 2063 2716 2282 2647 Day 57 Day 58 Day 59 Day 60 Day 61 Day 62 Day 63 Day 64 Day 65 Day 66 Day 67 Day 68 Day 69 Day 70 Day 71 Day 72 Day 73 Day 74 Day 75 Day 76 Day 77 Day 78 Day 79 Day 80 Day 81 Day 82 Day 83 Day 84 Day 85 Day 86 Day 87 Day 88 Day 89 Day 90 2955 2967 2687 2446 1526 1434 2467 1535 2423 1895 1483 2244 2210 2069 1551 1858 2243 2190 2554 1834 1822 2484 1703 2379 2040 1556 2327 1704 2783 2070 2402 2148 2582 1762 2632 1982 1259 969 2327 1537 966 2038 2110 2800 1951 1567 1831 2244 2478 1631 1691 1800 1447 2757 1160 1861 1285 1834 2241 1575 2290 3399 2024 2506 2900 1868 1413 2954 The data below are (annualized) daily rates of return on Microsoft stock. You are considering investing $1,000 in Microsoft. Based on the data below, predict how much your $1,000 investment will be worth in one year. Consider a worst case scenario. There is a 90% chance that, by the end of the year, your investment will be worth at least what amount? There is a 95% chance that, by the end of the year, your investment will be worth at least but not more than what two amounts? The data below show that the average return on MSFT is higher than the average return on DELL. What is the probability that this observed difference is simply due to random chance? Date 1-Jan 2-Jan 3-Jan 4-Jan 5-Jan 6-Jan 7-Jan 8-Jan 9-Jan 10-Jan 11-Jan 12-Jan 13-Jan 14-Jan 15-Jan 16-Jan 17-Jan 18-Jan 19-Jan 20-Jan 21-Jan 22-Jan 23-Jan 24-Jan 25-Jan 26-Jan 27-Jan 28-Jan 29-Jan 30-Jan 31-Jan 1-Feb 2-Feb 3-Feb 4-Feb 5-Feb 6-Feb 7-Feb 8-Feb 9-Feb 10-Feb 11-Feb 12-Feb 13-Feb 14-Feb 15-Feb 16-Feb 17-Feb 18-Feb 19-Feb 20-Feb 21-Feb 22-Feb 23-Feb 24-Feb 25-Feb 26-Feb 27-Feb 28-Feb 1-Mar 2-Mar 3-Mar 4-Mar 5-Mar 6-Mar 7-Mar 8-Mar 9-Mar Daily Rate of Return, MSFT (annualized) 9.8% 3.3% 6.6% 11.8% -0.8% 9.5% 0.8% 4.6% 8.7% 9.0% 4.8% 4.4% 2.2% 0.0% 6.2% 8.1% 5.5% 8.4% 4.3% 4.6% 9.3% 6.4% 11.1% 6.3% 9.1% 1.6% 9.0% 7.2% 11.5% 14.0% 6.4% 3.7% 5.9% 4.2% 7.0% -0.2% 8.4% 5.7% 3.8% 0.9% 13.0% 8.1% 0.2% 1.1% 10.1% 7.4% 8.5% 2.1% 3.4% 4.2% 12.2% 2.4% 1.2% 9.8% 5.8% 5.7% 8.9% 3.1% 5.9% 6.9% 12.0% 7.3% 6.2% 0.1% 5.6% 0.6% 4.5% 13.1% Daily Rate of Return, DELL (annualized) 3.8% 8.0% 5.8% 11.4% 6.7% 10.5% 1.5% 4.0% 2.6% 6.8% 5.3% 3.1% 7.0% 6.8% 4.0% 2.1% 8.8% 6.7% 8.5% 0.4% -3.0% 2.0% 0.8% 5.5% 0.4% -2.0% 2.0% 0.9% 2.8% 10.4% 1.4% 7.0% 3.5% 7.7% 9.9% 5.8% 6.1% 0.2% 3.6% 0.1% 4.4% 9.3% 4.9% 11.2% -1.0% 1.6% 15.1% 1.7% 9.1% 5.3% 7.0% 4.6% 10.6% 2.6% -0.3% 5.9% -4.7% 4.3% 1.7% 11.2% 5.5% 5.1% 4.5% 7.6% -0.9% 6.7% 3.8% 15.5% 10-Mar 11-Mar 12-Mar 13-Mar 14-Mar 15-Mar 16-Mar 17-Mar 18-Mar 19-Mar 20-Mar 21-Mar 22-Mar 23-Mar 24-Mar 25-Mar 26-Mar 27-Mar 28-Mar 29-Mar 30-Mar 31-Mar 1-Apr 2-Apr 3-Apr 4-Apr 5-Apr 6-Apr 7-Apr 8-Apr 9-Apr 10-Apr 11-Apr 12-Apr 13-Apr 14-Apr 15-Apr 16-Apr 17-Apr 18-Apr 19-Apr 20-Apr 21-Apr 22-Apr 23-Apr 0.2% 9.5% 1.2% 5.4% 11.6% 6.9% 7.2% 6.3% 2.0% 5.5% 13.3% 7.4% 10.8% 6.3% 4.5% 9.3% 4.3% 2.2% 7.0% 2.6% 6.9% 1.4% 3.9% 2.9% 2.1% 3.9% 8.5% 1.8% 2.8% 10.6% 1.9% 3.6% 7.5% 9.4% 5.6% 7.5% 5.6% 5.8% 6.8% 7.4% 5.6% 5.9% 6.1% 5.7% 5.5% 6.6% 3.0% 5.4% 10.5% 11.7% 4.7% 2.1% 7.4% 5.4% -1.2% -3.8% 6.8% 4.9% 8.4% 3.9% 4.0% 5.3% 0.4% 0.0% 0.7% 4.8% 3.0% 9.1% 8.1% 0.5% 8.2% 9.1% 8.8% 5.2% 7.2% 4.7% -0.6% 6.6% -3.4% 4.2% 4.0% -2.0% 4.9% 2.0% 4.8% 4.4% 6.6% 6.6% 8.9% 5.0% Your company is planning to build a 50,000 square foot warehouse. In an attempt to estimate the construction cost, you research the costs of recently built comparable warehouses in the area. That information is below. There is a 95% chance that the cost of your warehouse will be between what two extremes? Suppose your company constructs three warehouses. There is a 95% chance that the average cost per warehouse for the three warehouses will be between what two extremes? Comparable Warehouse Warehouse #1 Warehouse #2 Warehouse #3 Warehouse #4 Warehouse #5 Warehouse #6 Warehouse #7 Warehouse #8 Warehouse #9 Warehouse #10 Cost $7,500,000 $8,300,000 $6,900,000 $8,500,000 $6,800,000 $8,000,000 $7,100,000 $7,300,000 $7,500,000 $8,100,000