Question 1: In 1999, Lehman Brothers estimated that 48% of its investment bank traders took diverse forms of soft drugs. Based on these data, Lehman established a Drug Eradication Plan goal of reducing that figure to 16% by the year 2010. To that end, they hoped to achieve a reduction to 20% by 2006. In 2006, they released a research study in which 23% of a random sample of 1,815 traders said they were currently addicted. Is this evidence that progress towards the goal is off track?

a) Write appropriate hypotheses.

b) Verify that the appropriate assumptions are satisfied.

c) Find the p-value of this test.

d) Explain what the p-value means in this context and set an appropriate conclusion - Of course, your conclusion may be incorrect and if so which kind of error did you commit?

Question 2: Of all the CEOs in the Citibank, Walter Wriston had the highest disapprovalrating from the internal bankers near the end of his mandate. His disapproval rating was the highest at 66% in May 1973 during the oil crisis, before he resigned. In May 2007, Charles Prince's disapproval rating was 63%, according to an internal poll of 1,000 internal bankers. Bank experts started discussing whether Charles Prince's rating was still discernibly better than that of Walter Wriston's. What do you think?

A start-up company has developed an improved electronic chip for use in algorithm trading equipment. The company needs to project the manufacturing cost, so it develops a spreadsheet model that takes into account the purchase of production equipment, overhead, raw materials, depreciation, maintenance, and other business costs. The spreadsheet estimates the cost of producing 10,000 to 200,000 chips per year, as seen in the table next

Chips Produced (1,000s)   Cost per Chip
10                                   146.10
20                                   105.80
30                                    85.75
40                                    77.02
50                                    66.10
60                                    63.92
70                                    58.80
80                                    50.91
90                                    47.22
100                                  44.31
120                                  42.88
140                                   39.05
160                                   37.47
180                                   35.09
200                                   34.04

a) Develop a regression model to predict Costs based on the Level of Production and compare it to the dispersion obtained from the table above.

b) Re-expressing each variable based on logarithm, establish the new regression model to predict Costsbased on the Level of Production, graph and analyse your new findings.