The following table shows the yields (y) obtained in an agricultural experiment in tonnes per hectare after using (x) tonnes of fertilizer per hectare. Fertilizer (x, ton/hectare) 0 0.2 0.4 0.6 Yield (y, ton/hectare) 1.35 1.55 1.95 2.75 (a) Calculate the regression line of y on x (ie. y= a + bx)

(b) Calculate regression coefficient, rx,y

(c) Estimate the total yields in tonnes from a 2.2 hectare field if 0.5 tonne of fertilizer is used

Assume that you want to investigate the effects of TV commercials on a product. From the questionnaire survey so far, we know the followings.

1. The probability that a purchaser of the product has watched the TV commercial is A.

2. The probability that a non-purchaser of the product has watched the TV commercial is B.

3. The probability that a customer buys the product is 0.1.

Let A = 0.6 and B = 0.2.

Question: What is the probability that a customer who has watched the TV commercial buys the product? ( Answer in the decimal form, not the fractional form.)

3 SHOW ALL WORK STEP BY STEP WITHOUT SHORT CUTS

1) make a solution of 0.25% n-propanol (use 25 ml volumetric flask)

2) make a water solution of methanol and isopropanol of 0.2% make it in the same container and in separated container.

3) make a 50ml stock solution of 0.50 wt% ethanol .

4) make five solution ranging from of ethanol 0.0 %, 0.05%, 0.10%, 0.20,% 0.30% 0.40% 0.50% wt% in water. (Used 25ml volumetric flasks)

Depreciation rate for all equipment is 0.2 and tax rate is 35%. Cost of capital is 8%

a. What is the NPV of each project Edgar, Justin , and Monique

b. Which project is the best to use? (Hint: Use equivalent annual annuity or replacement chain method to answer this question)

Head to www.bls.gov and select Multifactor Productivity from the Subject drop-down menu. Scroll down and select the PDF version of the

Multifactor productivity decreases 0.2% in 2016, first decline since 2009..  

1. What has been the general trend for multi-factor productivity in the U.S. over the past 15 years?

2. What does this trend suggest has happened to production functions in the U.S.?

3. Assuming this change in productivity has happened to all firms, how will this change in productivity affect cost curves?

A potato chip company advertises that their family sized bag of potato chips have an average weight of 10 oz. I want to know if the bags are overfilled. I randomly sampled 100 bags of chips and find that my sample has a mean weight of 10.1 oz and a standard deviation of 0.2 oz. The sample data was not strongly skewed.

1. Write the appropriate null and alternative hypothesis.

2. Calculate the t score.

3. use the t score to evaluate the strength of the evidence against the null hypothesis.

The amount of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of 0.2 ounces (these are the population parameters). Suppose a sample of 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 10.6 ounces. (Hint: think of this in terms of a sampling distribution with sample size = 100)

a. 0.6915

b. 0.3085

c. 0.1595

d. Approximately 0

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 15% and a standard deviation of return of 25%. Stock B has an expected return of 12% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.2. The risk-free rate of return is 1.5%.

1) Approximately what is the proportion of the optimal risky portfolio that should be invested in Stock B?

2) What is the Expected Return on the Optimal Portfolio?

3) What is the REWARD to VARIABILITY Ratio of the Optimal Portfolio?

A spring mass system with a natural frequency fn = 12 Hz is attached to a vibration table. The table is set to vibrate at 16 Hz, 0.5 g maximum acceleration:

a. What is the amplitude of the table's motion in inches?

b. What is the magnification factor M of this undamped system?

c. What is the maximum displacement of the mass assuming no dampening?

d. What is the maximum acceleration of the mass assuming the packaging can be modeled as a viscous damper with a damping ratio of 0.2?

e. Is the motion of the mass in phase or out of phase with the motion of the table?

The payoff table below provides the profits (in thousands of dollars) for each of four alternatives in each of three supplies.

Suppose that the probabilities for the supplies above are P(S₁) = 0.6, P(S₂) = 0.2, and P(S₃) = 0.1.

1. Which alternative should be selected under Bayes’ Rule?
2. What is the expected value of perfect information for this decision?