You are doing an internship with Macy’s and are tasked with forecasting sales so that you can make inventory orders. You have weekly sales data for men’s dress shirts in your store from each of the past six weeks. You decide to try both a 3-period moving average and exponential smoothing with λ = 0.7 to see which model is more accurate and then use that one to make forecasts. The sales data is shown below.

What is the calculated MSE for the exponential smoothing method? Round intermediate calculations and final answer to 4 decimals.

What is the calculated MSE using the 3-period moving average? Round intermediate calculations and final answer to 4 decimals.

1. A contractor is planning to use a crawler tractor with power shift transmission to push 1,500 LCY. The tractor must haul the loose material up a 12% slope where it will be stockpiled for later removal. The contractor has measured the tractor blade load measurement: the pile length 12.6 ft, the pile width 8.1 ft, and the pile height 4 ft. The tractor weighs 44,400 pounds, and the coefficient of traction is estimated to be 0.7. The average haul distance is estimated to be 300 ft. The job efficiency is 50 minutes per hour. Performance characteristics of the tractor are shown in the lecture slides. (Note: 1 mi/hr = 88 ft/min).

1) What is the estimated productivity of the tractor? (First gear for dozing; Third gear for return.)

2) Estimate the total hours to complete the work.

3) Determine if the tractor can perform the work in the given condition above.

There is evidence that cytotoxic T lymphocytes (T cells) participate in controlling tumor growth and that they can be harnessed to use the body's immune system to treat cancer. One study investigated the use of a T cell-engaging antibody, blinatumomab, to recruit T cells to control tumor growth. The data below are T cell counts (1000 per microliter) at baseline (beginning of the study) and after 20 days on blinatumomab for 6 subjects in the study. The difference (after 20 days minus baseline) is the response variable.

Do the data give evidence at the 5% level that the mean count of T cells is higher after 20 days on blinatumomab?

The test statistic is t =  (±±0.001)

(please type not write down the answer) astronomy

3. A main sequence star of mass 15 M⊙ has a luminosity of approximately 10,000 L⊙ . a. At what rate does mass vanish as H is fused to He in the star’s core? Note: When we say “mass vanish” what we really mean is “gets converted into energy and leaves the star as light”. b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare to the lifetime of the Sun. It should be much, much shorter.

1. A marksman hits a target 0.73 of the time. He fires 10 shots at the target. Find the probability that he make exactly 8 hits using the binomial distribution.

3. The campus bookstore asked a random set of freshmen (group 1) and seniors (group 2) as to how much they spent on textbooks in that term. The books store would like to test if the average spending of Freshmen is at least $5.0 more than that of seniors. Which of the following is the correct alternative hypothesis (H1)?

6. Scores on a standard test are normally distributed with a mean of 37.3 and a standard deviation of 8. Find the probability that the score is between 37 and 42.
7. Let X be a continuous random variable whose probability density function is:    f(x) = 1.5 x²   for -1 < x < 1 and 0 else where.

Find the probability that the random variable is between -1.6 and -0.7.

HOUR DEADLINE PLEASE HELP

The energy flux of solar radiation arriving at Earth orbit is 1353 W/m2. The diameter of the sun is 1.39x109 m and the diameter of the Earth is 1.29x107 The distance between the sun and Earth is 1.5x1011 m.

(a) What is the emissive power of the sun as calculated from the parameters given above?

(b) Approximating the sun’s surface as black, what is its temperature (as calculated from the parameters given above)?

(c) At what wavelength is the spectral emissive power of the sun a maximum?

(d) Assuming the Earth’s surface to be black and the sun to be the only source of energy for the earth, estimate the Earth’s surface temperature. Assume that the Earth absorbtivity to solar irradiation is 0.7. The actual average temperature of the Earth is currently ~288 K. Why do you think there are differences between your prediction and the actual average temperature (assume that the given value of absorbtivity is correct)?

A process for making small amounts of hydrogen by cracking ammonia is being considered, and residual uncracked ammonia is to be r removed from the resulting gas. Design a tray type absorption column to remove NH₃ from a gas stream using water as solvent. The gas stream (flow rate = 0.7 kg/s) consists of H₂ and N₂ (in the molar ratio 3: 1) and 3% NH₃ by volume. The ammonia will be removed by scrubbing the gas countercurrently with pure liquid water (flow rate = 6 kg/s) in a sieve-tray tower. The exiting gas stream should have 1% NH₃. Assume that only NH₃ can dissolve in water, and other gases (N₂+H₂) are inerts. Conditions at bottom of tower: Temperature, T = 303 K, and Pressure = 200 kPa.

Determine:

The number of stages (trays), tray spacing, and the diameter of the absorption column

#1 A mass measurement system behaves as a second-order system (consisting of a mass = 50g, a spring, and a viscous damping element). To determine the damping the ratio, the system was exposed to a step input and decaying oscillating amplitude of the system output was measured. Results of these measurements showed that the damping ratio = 0.7 and the ringing frequency f_d =389 Hz. Calculate the following and report results using 3 significant digits minimum:

The natural frequency, in Hz

The spring constant, in kN/m

Logarithmic decrement ln(x₁/x_n)

The period of oscillation when the system is exposed to a step input, in milliseconds

The dynamic error, ?, at 450 Hz in % (include the sign of the error)

The phase and time delay between input and output for sinusoidal inputs of 450 Hz in rad and milliseconds, respectively

Can we use this system to measure mass in outer space? How? Use a diagram to explain.

Do the following using R. You must also turn in a copy of your R code.

(10) What is the probability a beta (1, 8) random variable is less than 0.13?

(11) What is the probability a beta (3, 9) random variable is greater than .4?

(12) What is the probability a beta (18,4.4) random variable is between 0.6 and 0.7?

(13) At what value of x is the probability that a beta (4, 7) random varable is less than x equal to .71? That is, for what x is P r(beta(4, 7) random variable < x) = .71?

(14) At what value of x is the probability that a beta (12.2, 25.7) random variable is less than x equal to .2? That is, for what x is P r(beta(12.2, 25.7) random variable < x) = .2?

You are signed up for Comcast internet service. This service requires a physical device, a cable modem, to connect you to the provider's internet service. You have two options:

1. buy the cable modem on the internet, this will cost about $100

2. rent the cable modem from the provider, this will cost about $10/month.

Assume the relevant investment rate of return is 0.7% APR on your money (this is petty cash, and would just be sitting in your high-interest savings account at best). Assume the lifetime of the device is 6 years.

What is net benefit to you of buying the device as compared to renting it?

Hint: find the present value of all the estimated rent payments for the lifetime of the device. compare to the present value of buying it outright. the 'benefit' may be positive or negative, depending on whether you give up more present-wealth renting or buying.