Consider an i.i.d. random sample of size 3 denoted by ?1,?2, ?3 from the same population, where the mean ? and variance ? 2 are unknown. Suppose that you have the following two different estimators for mean ?. (Remember: no work, no credit.) ?̂1 = 0.3?1 + 0.5?2 + 0.2?3 ?̂2 = 0.5?1 + 0.5?3 a. Is ?̂1 unbiased? b. Is ?̂2 unbiased? c. Which one is preferred, ?̂1 or ?̂2?

Data for the mean mass of various animal species and their corresponding metabolic rate is provided below. It is believed that the data follows the power model. i.e. ?????????? = ? (????)? where α and β are the regression coefficients.

Show by hand with pen and paper the linearisation of this nonlinear model.

A piston–cylinder device contains steam that undergoes a reversible thermodynamic cycle. Initially the steam is at 400 kPa and 350oC with a volume of 0.3 m3. The steam is first expanded isothermally to 150 kPa, then compressed adiabatically to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine (a) the net work and heat transfer for the cycle after you calculate the work and heat interaction for each process and (b) show the cyclic process on a PV diagram

1. A 4 kg mass is resting on a ramp inclined at an angle of 30 degrees with respect to the horizontal. A string is attached to the 4 kg mass and passes over a frictionless pulley and is connected to a 5 kg mass hanging over the side. If the coefficient of friction between the ramp and the 4 kg mass if 0.3 find; A) The acceleration of both masses B) The tension in the string C) Find the speed of both blocks after they move a distance of 2 meters.

1. Describe the meaning of the molecular equation between the NaOH and HCl solutions on the microscopic and macroscopic scales.
2. Provide a detailed description for titrating the calculated volume of HCl solution with the 0.3 M NaOH solution. Make sure to describe what equipment you would use, how it is used and which characteristics of the equipment make them suitable for this purpose.
3. Consider the properties of HCl solutions. Identify reasons why it needs to be titrated to determine its actual concentration.

A team of USGS scientists detected a plume of the soil fumigant 1,2-dichloro-propane (DCP) in the groundwater flowing away from a field. The aquifer solids have an fOC (organic carbon content) of 0.6%, a solid density of 2.66, and a porosity of 0.3. If DCP partitions fast between OC and water, and if partitioning into OC is the main process that slows down DCP transport estimate the retardation factor Rf. log KOC [L/kg] = 2.28 for DCP.

Refer to the accompanying data​ table, which shows the amounts of nicotine​ (mg per​ cigarette) in​ king-size cigarettes,​ 100-mm menthol​ cigarettes, and​ 100-mm nonmenthol cigarettes. The​ king-size cigarettes are​ nonfiltered, while the​ 100-mm menthol cigarettes and the​ 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the​ king-size cigarettes are not​ filtered, do the filters appear to make a​ difference?

King-Size   100-mm_Menthol   Filtered_100-mm_Nonmenthol
1.4   1.2   0.7
1.1   0.9   1.0
1.0   1.2   0.4
1.1   0.9   1.1
1.4   1.2   1.1
1.2   1.3   0.7
1.3   0.9   1.0
1.0   1.1   1.2
1.2   0.9   0.8
1.2   0.8   0.9

1. Determine the null and alternative hypotheses.

2. Find the F statistic.

3. Find the P value.

4. What is the conclusion for this hypothesis test?

A. Reject H 0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

B. Fail to reject H 0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

C. Reject H 0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

D. Fail to reject H 0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine

5. Do the filters appear to make a difference?

A. ​No, the filters do not appear to make a difference because there is sufficient evidence to warrant rejection of the claim.

B. No, the filters do not appear to make a difference because there is insufficient evidence to warrant rejection of the claim.

C. The results are inconclusive because the​ king-size cigarettes are a different size than the filtered cigarettes.

D. Given that the king dash size cigarettes have the largest mean comma it appears that the filters do make a difference left parenthesis although this conclusion is not justified by the results from analysis of variance right parenthesis .

You have an opportunity to purchase the 23 site Plum Creek manufactured home/RV park for $250,000. The park caters to extended stay residents (six months or longer) and charges a market rental rate of $240 per site per month. You expect to be able to raise site rentals 3% per year to account for inflation. There are no tenant reimbursements or passthroughs. You plan a five year holding period so you create a six year proforma. The owner reports an annual vacancy rate of 10% but you believe an annual 15% vacancy rate every year of the holding period is a more realistic estimate. You use 15%. For expense estimates, you rely on public records (tax office), an income/expense statement provided by the owner/seller, and Darrell Hess & Associates, a national manufactured home park brokerage company that compiles expense data from hundreds of parks nationwide. The previous year’s property taxes were $5,042. The new assessment and tax rate has not been set, so the previous year’s taxes are used in your pro-forma for the first year. Hazard and liability insurance is estimated to be 2% of effective gross income (EGI) in first year. Each site is individually metered for electricity and the tenants are responsible for their usage. The park owner reported annual water and trash removal expenses of $5,460 for the previous year, and this amount appears reasonable for your first year projection. The annual administrative/management expense (part time on-site manager, advertising, legal fees, accounting fees and office expenses, etc.) is estimated to be 29% of EGI by Darrell Hess & Assoc. The owner did not report any maintenance expense as he did all of the work himself. You believe a $2,000 first year expense is reasonable for the road maintenance, landscape maintenance, etc. You expect expenses to increase 3% each year of the five year holding period except insurance and management expenses tied to EGI. Page 7 of 7 You have obtained a loan commitment from a bank for 80% (20% down payment aka equity contribution) of the purchase price with a 20 year amortization at 6% interest. 1) Create a six year Pro-forma statement of cash flows on an Excel spreadsheet. 2) Calculate the following ratios and indicators (all before tax) by Excel formulas at the bottom of the spreadsheet to three decimals: A) Operating expense ratio (annual operating expense/EGI); according to Darrell Hess & Associates, operators can expect a 50% operating expense ratio. B) All Five Years of Debt Coverage Ratio (NOI/debt service); 1.3 or greater is considered good by the lender. C) All Five Years Return on Equity (BTCF/equity invested); investor surveys indicate 13% or better is expected for each year. D) Using the IRV formula, calculate the indicated overall rate (cap rate) RO for Year One to see if it is within the 9-11% range for manufactured home parks indicated by a national investor survey. Use the $250,000 asking price as the value in IRV for the calculation. E) Calculate the value of the subject after the five year holding period (the reversion) using a 10.5% terminal RO. Remember to carry the pro-forma to a sixth year to obtain Year Six NOI. F) Calculate the unleveraged IRR of the cash flows using the $250,000 asking price. G) Calculate the NPV of the property using a 12% IRR

4. Consider a reheat–regenerative vapor power cycle with two feedwater heaters, a closed feedwater heater and an open feedwater heater. Steam enters the first turbine at 12.0 MPa, 520C and expands to 0.6 MPa. The steam is reheated to 440C before entering the second turbine, where it expands to the condenser pressure of 0.006 MPa. Steam is extracted from the first turbine at 2 MPa and fed to the closed feedwater heater. Feedwater leaves the closed heater at 200C and 8.0 MPa, and condensate exits as saturated liquid at 2 MPa. The condensate is trapped into the open feedwater heater. Steam extracted from the second turbine at 0.4 MPa is also fed into the open feedwater heater, which operates at 0.3 MPa. The stream exiting the open feedwater heater is saturated liquid at 0.3 MPa. The net power output of the cycle is 100 MW. There is no stray heat transfer from any component to its surroundings. If the working fluid experiences no irreversibilities as it passes through the turbines, pumps, steam generator, reheater, and condenser, determine (a) the thermal efficiency, (b) the mass flow rate of the steam entering the first turbine, in kg/h. (Turbine and pump isentropic efficiencies 100% & Create a table of all values)

4. NFL Combine

The 40-yard dash time (i.e. the amount of time it takes to run 40 yards of the prospective NFL running backs is normally distributed with a mean of 4.53 seconds and a standard deviation of 0.2 seconds. For the corner backs, it is also normally distributed with a mean of 4.46 seconds and a standard deviation of 0.3 seconds.

(a) Find the probability that a running back finishes the 40 yard dash between 4.33 and 4.73 seconds.

(b) Find the probability that a randomly selected running back outruns a randomly selected corner back (i.e. the probability that the running back completes a 40 yard dash more quickly than a corner back).

(c) Find the probability that a random sample of n=25 corner backs will have an average dash time of less than 4.40 seconds.

(d) Suppose that a single line backer (not a corner back and not a running back- so you don't know the population mean or variance) ran 41 40 yard dashes, over the course of one week. His average time over these 41 trials was 4.50 seconds and the standard deviation was 0.3 seconds. Find a 95% confidence interval for the mean of his true 40 yard dash time.