Number 5 (8 pts) An analysis of variance on the mean number of hours that Glendon students sleep the night after consuming either one of two different brands of energy drinks or an herbal tea at lunch indicates that the means are not all the same. Further data is gathered, with the following results

Use a contrast to test at a 5% level of significance whether the energy drinks lead to a lower number of mean hours of sleep than the herbal tea.

Compare the yearly greenhouse gas emissions from 1 GWe (gigawatt-electric) power stations powered by natural gas and wind turbines. The energy content of natural gas is 55 MJ/kg, and the electrical converting efficiency is 40%. Wind turbines do not emit CO₂ as they harness the wind but emissions do occur during the manufacturing of the turbine. For USA, assume the CO₂ emission per GDP is approximately 500 Tonnes / $ 1 million of GDP. For wind turbines, it costs $2 million for a 1 MWe plant, which has an efficiency of 0.3, and the yearly maintenance is approximately 2% of the initial cost. Assume the average lifetime of a wind turbine is 20 years.

Income at the architectural firm Spraggins and Yunes for the period February to July was as follows:                                                          

Assume that the initial forecast for February is 70 ​(in $​ thousands) and the initial trend adjustment is 0. The smoothing constants selected are alpha (α) ​= 0.1 and beta (β) ​= 0.3

1) Using​ trend-adjusted exponential​ smoothing, the forecast for the architectural​ firm's August income is _______ thousand dollars ​(round your response to two decimal​ places).

2) Compute the MSE for the forecast developed using​ trend-adjusted exponential smoothing. ​(Round your response to two decimal​ places.)

A vehicle which is equipped with a 6 cylinder, 2000 cc spark ignition engine is cruising at an average speed of 150 km/h from Ankara to Istanbul on the highway. The mass of the vehicle with single driver is 1200 kg and its projected frontal area is 3 m2. The coefficient of rolling resistance is 0.015 and the discharge coefficient is 0.3. The distance between Istanbul and Ankara is approximately 450 km. Assuming an average brake specific fuel consumption of 250 g/hp-h, calculate how many liters of fuel will be used during this journey ( r fuel = 0.73 g/cc and ambient air density r a=1.2 kg/m3).

1. Consider a stock with the following return information for 2015-2020

Year    Return

2015    25%

2016    -15%

2017    3%

2018    41%

2019    -6%

2020    12%

Find the following for your sample of returns: Average Return, Variance, and Standard Deviation.

2. Jamie’s portfolio consists of $15,000 in Microsoft stock and $45,000 in Coca Cola. Microsoft has an expected return of 19% annually with a standard deviation of 42%. Coca Cola has an expected return of 10% annually with a standard deviation of 20%. The correlation between the 2 stocks has been 0.3.

a) Calculate the expected return of Jamie’s portfolio

b) Calculate the standard deviation of Jamie’s portfolio

Consider a continuous culture of Bacillus subtilis bacteria, which are used to produce the enzyme amylase during the growth phase. The relevant parameters for growth of this bacteria are μ_MAX = 0.88 hr^-1, Y_X/S = 0.5 gdw/gr substrate, S₀ = 4.0 gr substrate/L, and the Monod constant K_S = 0.3 gr/L, while the protein yield during growth phase is Y_P/X (aka product parameter α) = 0.12 g protein/gdw. The chemostat is operated at a dilution rate that is 60% of the maximum growth rate. Using this information, what is the steady state rate of product formation in the chemostat culture, in units of grams protein/L-hour?

How do I find T score and Stanine when (Xbar = 66.73, σ = 5.77)

2. Adapted from Exercise 3.19 in the textbook. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 266 days and standard deviation 16 days.

(a) Between what range of days do about 95% of pregnancies last?

(b) What proportion of pregnancies last more than 170 days?

(c) What proportion of pregnancies last less than 245 days? 1

(d) What proportion of pregnancies last between 245 and 280 days?

(e) A pregnancy that lasts an amount of time 0.3 standard deviations less than the means lasted for how many days?

Star Corp has 5 million shares outstanding and no growth opportunities. It just paid a dividend of $6 per share and has a market value of $62.5 million.

a. What is the discount rate on Star’s stock?

b. The firm has an opportunity to invest in a new project. The project requires an additional investment of $1.2 million today and will generate additional earnings in the next 10 years. The first earnings amount of $0.3 million will begin one year from now and grow at 4% each year thereafter (until year 10). Assuming no taxes, calculate the NPV of the new project.

c. What will the stock price be if the firm undertakes the new project?

You are researching a population of brittle stars that varies in the number of legs that they produce. You survey the local population, and come up with the numbers below. Assume that the phenotypes you encounter represent the full range of possible phenotypes in this population.

1. Calculate the phenotypic variance in this trait.
2. Do the traits in this population appear to be normally distributed? Give an explanation of why this pattern might be observed.

3. Through a series of breeding experiments, you calculate that h2 for this population is 0.3. If no dominant alleles contribute to this trait, and there are no epistatic interactions involving the gene loci that control this trait, what is VE for this population?

#of legs: # of individuals:

5 ; 420

6 ; 189

7 ; 72

8 ; 5

9 ; 3