3The data for initial hindered settling velocities of a suspension are given in the following table. a)Size the area of a clarifier to handle a flow of 2300 m3/d containing a Total Suspended Solids (TSS) concentration of 2100 mg/L. The underflow SS. Concentration is 10 000 mg/L. b)What is theflowrate of the underflow?

C, mg/L1000 2000 4000 6000 8000 10000 15000
V, m/h 3.74 2.82 2.26 1.04 0.49 0.25 0.072

Consider the dataset regarding the drop in light percent output (output) and two input variables – bulb surface (qualitative) and length of the operation hours (quantitative). The data is available in a sheet named ‘Problem 3’. Answer the following.

(a) Write down the overall model form if one wishes to build a second order model for each value of the qualitative variable

(c) Build a regression model showing the 90% confidence ranges of the regression parameters. Write down the mean estimates of the regression parameters for the model in (a)

(d) Write down the 90% bounds of the estimate of the y-intercept (constant term)
(e) Compute the model prediction for a bulb with a dirty surface and with 1500 operation hours.

(f) Perform one-way hypothesis testing for the existence of ?2 term, where ?2 is the qualitative input. Use ? = 0.05

DATA

Here are the figures for the loyalty of a sample of imperial soldiers on the Death Star:

Please fill in the appropriate totals:

Assuming these totals, what counts would be expected in each cell (to two places after the decimal) if soldier type and loyalty status were independent?

Assuming soldier type and loyalty status are independent, fill in (two two places after the decimal) each chi-square contribution:

What is the value of the chi-square test-statistic (to one place after the decimal)?

Using an online chi-square calculator, what is the p-value for this rounded chi-square value?

Do we have evidence at the 10% level that soldier type and loyalty status (for all Death Star soldiers) are dependent (0 = no, 1 = yes)?
Do we have evidence at the 5% level that soldier type and loyalty status (for all Death Star soldiers) are dependent (0 = no, 1 = yes)?
Do we have evidence at the 1% level that soldier type and loyalty status (for all Death Star soldiers) are dependent (0 = no, 1 = yes)?

Materials:

Reaction Buffer 0.5 M Tris HCl pH 8.0 with 5 mM MgCl2

Alkaline phosphatase: 500 μg/mL stock solution in the buffer above. Keep enzyme on ice!

p-nitrophenyl phosphate: 1000 μM and 10000 μM stock solutions in reaction buffer

1) Using the enzyme stock solution above and the dilution equation, calculate the volumes needed to prepare 2 mL of three enzyme dilutions consisting of 100 μg/mL, 125 μg/mL, and 150 μg/mL. Use the reaction buffer to make these dilutions.

2) Calculate the amount of substrate needed for each of the following concentrations 10 μM, 25 μM, 50 μM, 100 μM, 200 μM, 500 μM, 1000 μM, and 2000 μM using the two stock solution concentrations listed above. Use the 1000 μM stock solution to calculate dilutions from 10-200 μM and the 10,000 μM stock solution to calculate from 500 μM-2000 μM. The final volume is 1.0 mL (or 1000 μL) for each dilution. Also calculate the volume of buffer needed, given that we will add 100 μL of the enzyme solution and the final volume is 1.0 mL (or 1000 μL) for each dilution.

1. Use either a shift in demand of supply to GRAPHICALLY represent each of the following situations. Also, label the graphs correctly and indicate the changes in equilibrium in each case.

1. Beef market:  Increases in the cost of cattle feed.
2. Air travel market: Reduced number of travelers due to Covid-19 pandemic.
3. SUV market: Reduced gasoline prices.
4. Smartphone market: Technology improvements reduced the cost of manufacturing smartphones.

Four separate graphs please.

2. a) How would economic contraction brought about by Covid – 19 slowdown be represented using production possibilities curve?

b) Repeat a) for improved technology which results in increased productivity?

3. Good                Quantity           Price in 1999                Price in 2000

X                      10                    $5                                $6

Y                      20                    $10                              $10

Z                      5                      $6                                $10

1. Calculate the market basket value for each year. What is the consumer price index in 1999?
2. What is the inflation rate between 1999 and 2000?

Show all calculations for full credit.

b) In a given year, there are 10 million unemployed workers and 120 employed workers the country of Landia. Calculate the unemployment rate in Landia.

120/10,000,000 = 0.0012%

1-0.0012 = 0.9988

0.9988*100 = 99.88

Unemployment rate = 99.88%

Show all your calculations for full credit.

The index of industrial production ( t IP ) is a monthly time series that measures the quantity of industrial commodities produced in a given month. Suppose that an analyst has data on this index for the United States. The analyst begins by computing Y subscript t = 1200 X ln IP subscript t / IP subscript t-1 , which gives the monthly percentage change in IP measured in percentage points at an annual rate. The analyst estimates an AR(4) model for industrial production growth and then augments that model with four lagged values of ?Rt , where Rt is the interest rate on three-month U.S. Treasury bills (measured in percentage points at an annual rate). All regressions are estimated over the sample period 1960:1 through 2000:12 (that is, January 1960 through December 2000). (a) The Granger causality F statistic on the four lags of ?Rt is 2.35. Do interest rates help to predict IP growth? Explain your answer. 2 (b) The analyst also regresses ?Rt on a constant, four lags of ?Rt , and four lags of IP growth. The resulting Granger causality F statistic on the four lags of IP growth is 2.87. Does IP growth help to predict interest rates? Explain your answer.

Question 1: Problem solving

A handicraft products trader is selling leather cases for $40 the unit. To run his business, he needs to pay $10000 for rent, $5000 salaries, and another $5000 for marketing campaigns. The handicraft trader has the choice to import his products from different countries, and it will cost him $20 per unit if the product comes from China, $25 per unit if the product comes from India, and $15 per unit if the product comes from Malaysia.

Questions:

1. If the trader must choose to import his products from one country, then which country will it be?
2. compute the trader’s profit if he sells 40 units imported from China and 50 units imported from India.
3. compute the trader’s profit if he imports only from China and sells 500 then 2000 units. Explain the obtained results.
4. What is the trader total cost from importing 100 units from Malaysia and 200 units from India ?
5. If the trader decides to import only from China, how many units he should sell to reach a profit of $2000?
6. If the trader wants to reach a positive profit in case of selling 900, 110, and 1500 units, then from where he should import his products for each case.

1. By January 2014 the US population had grown to 317.3 million and the US Federal Debt was a reported $17.3 trillion. Calculate the January 2014 Federal Debt per capita and use the calculation in a meaningful sentence.

2. From class we learned that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million. Use these values to compute the federal debt per capita in 2010.

3. In 1980, a Domino’s large pizza cost $4.99. What would be the cost of that pizza in 1995 dollars?

4. In 1986, a certain model of car cost $13,000. What would be the cost of that car in 2012 dollars? How does this compare to the actual cost of a typical new car in 2012?

5. According to a NY Times article on December 13, 2009, the average selling price of a 32” LCD TV was $600. What would be the cost of that same TV in 2015 dollars?

6. In 2009, the price of a package of crayons was $2.80. If it was the year 1988, what would the price be?

7. Use the chart below to answer: Using the starting value of $112 in 1995, which year was a better price when considering inflation? 2000, 2007 or 2011? (Assume that 1995 is a fair value for the goods and services.)

For each of the questions below, a histogram is described. Indicate in each case whether, in view of the Central Limit Theorem, you can be confident that the histogram would look like approximately a bell-shaped (normal) curve, and give a brief explanation why (one sentence is probably sufficient).

1. The price of one gallon of gasoline at a particular gas station is recorded every day of the year, and the 365 values are plotted in a histogram.

2. Two hundred students in a statistics class each flip a coin 40 times and record the number of heads. The numbers of heads are plotted in a histogram.

3. Two hundred students in a statistics each roll a die 60 times and record the sum of the numbers they got on the 60 rolls. They make a histogram of the 200 sums.

4. One thousand randomly chosen people report their annual salaries, and these salaries are plotted in a histogram.

5. The day before an election, fifty different polling organizations each sample 2000 people and record the percentage who say they will vote for the Democratic candidate. The 50 values are plotted in a histogram.

6. The fifty polling organizations also record the average age of the 2000 people in their sample, and the 50 averages are plotted in a histogram.

7. One hundred batteries are tested, and the lifetimes of the batteries are plotted in a histogram.

Below are data for countries with fast and slow growth rates over two different time periods. Construct a bar chart for each country in both categories. In other words, you will end up with four different bar charts, two for each of the two categories of the countries representing both time periods.