The partial pressure of oxygen in the lung alveoli is a bit lower than in ambient air, being about 100 mm of mercury, or 0.13 Atm (it is lower than the partial pressure in air mainly because oxygen is continually taken up by the alveolar capillaries and carbon dioxide is continually released into the alveoli).  In cell-free blood plasma (or a saline solution formulated to match key characteristics of blood plasma), which lacks red blood cells and therefore lacks hemoglobin, the concentration of oxygen will equilibrate at 37° C at about 0.3 ml O₂/100 ml plasma. For whole blood (with hemoglobin), however, the O₂ concentration is around 20 ml O₂/100 ml whole blood.

By what factor does the presence of hemoglobin increase the oxygen content of blood?

B.  Given the above, imagine that you are an emergency room physician treating a patient who lost a quarter of his blood in an accident. A paramedic replaced this lost blood with saline solution to keep his blood pressure up. The saline solution contains no hemoglobin since it contains no red blood cells. The patient is short of breath and oxygen levels in his blood are dangerously low. If for some reason you must choose between administering pure (100%) oxygen or giving a transfusion of whole blood to restore the red blood cell count, which would you expect to be more helpful? Address this decision by answering the questions below. Show your work and be as quantitatively explicit as possible.

1. Under normal conditions, what percentage of blood oxygen content is accounted for by oxygen dissolved in the plasma and what percentage is bound to hemoglobin? By how much do these percentages change after the patient has a quarter of his blood volume replaced with saline solution?
2. a) By what percentage could total blood oxygen content be increased by delivering pure (100%) oxygen instead of allowing the patient to simply breathe ambient air? Assume that Henry’s Law applies.

b) One obviously can’t deliver oxygen at a concentration higher than 100%, but how else might the partial pressure of the oxygen being delivered be modified to increase the amount diffusing into the blood?

3. By what percentage could blood oxygen content be increased by transfusing whole blood to restore the red blood cell count? Relative to delivering pure oxygen, is this a more promising or less promising approach for restoring normal blood oxygen levels? Explain.

A company assembles and sells skateboards. One popular model is the "ICE". The final assembly plan for April to September, which also represents 50% of a full year’s demand:

The company is using MRP. The forecast for Skateboard ICE for the next coming six weeks:

The company are buying all components from different suppliers. They are only making the wheel assembly and the assembly of the final skateboard, see also the diagram above.

The company has an ordering cost of $150/order and the inventory carrying cost is estimated to 10%.

3a. If we use moving average with n=5, what is the forecast for Skateboard ICE for October?

3b. If we use exponential smoothing with α=0.3, what is the forecast for Skateboard ICE for October?

3c. Suppose it's now week 35. In what week should production of wheel assemblies start?

3d. In relation to question 3c above, what quantity of wheel assemblies will be needed?

3e. The company have had some problems with the supplier of the truck parts and therefore want to review the setup. But first they want to check how many truck parts they should order each time by calculating the Economic Order Quantity (EOQ).

What quantity of truck parts should the company order?

3f. The supplier of the truck parts replies to the company that if they order in lots of 10 000 each time, they will get a 5 % discount.

What is the total cost for the truck parts if the company order 10 000 each time?

An assistant in the district sales office of a national cosmetics firm obtained data on advertising expenditures and sales last year in the district’s 44 territories.

X1: expenditures for point-of-sale displays in beauty salons and department stores (X$1000).

X2: expenditures for local media advertising.

X3: expenditures for prorated share of national media advertising.

Y: Sales (X$1000).

1. Test the regression relation between sales and the three predictor variables. State the hypotheses, test statistic and degrees of freedom, the p-value, the conclusion in words.

2. Determine whether the linear regression model is appropriate by using the “usual” plots (scatterplot, residual plots, histogram/QQ plot). Explain in detail whether or not each assumption appears to be substantially violated.

An assistant in the district sales office of a national cosmetics firm obtained data on advertising expenditures and sales last year in the district’s 44 territories. Data is consmetics.csv. Use R. I don't want answers in Excel or SAS :)

X1: expenditures for point-of-sale displays in beauty salons and department stores (X$1000).

X2: expenditures for local media advertising.

X3: expenditures for prorated share of national media advertising.

Y: Sales (X$1000).

6. (4) Are there any influential points?

7. Is there a serious multicollinearity problem?

(3) Include an appropriate scatterplot and correlation values between the explanatory variables.

(3) Judge by VIF, do you think there is a problem with multicollinearity? (Hint: VIP or tolerance)

(3) Compare your answers in parts i and ii. Are your conclusions the same or different? Please explain your answer.

Data:

Flexible Budgeting and Variance Analysis

I Love My Chocolate Company makes dark chocolate and light chocolate. Both products require cocoa and sugar. The following planning information has been made available:

I Love My Chocolate Company does not expect there to be any beginning or ending inventories of cocoa or sugar. At the end of the budget year, I Love My Chocolate Company had the following actual results:

Required:

1. Prepare the following variance analyses for both chocolates and the total, based on the actual results and production levels at the end of the budget year:

     a. Direct materials price variance, direct materials quantity variance, and total variance.

     b. Direct labor rate variance, direct labor time variance, and total variance.

Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

2. The variance analyses should be based on the standard  amounts at actual  volumes. The budget must flex with the volume changes. If the actual  volume is different from the planned volume, as it was in this case, then the budget used for performance evaluation should reflect the change in direct materials and direct labor that will be required for the actual  production. In this way, spending from volume changes can be separated from efficiency and price variances.

When an airbag explodes, there are 3 different types of reactions that occur. Sodium azide produces nitrogen gas but there is a bi-product of Na. Na is very reactive and must be neutralized. For this, potassium nitrate is used. This creates two further compounds, sodium oxide and potassium oxide, which must be neutralized by silicon dioxide.

Chemical reactions:

1. Sodium Azide is ignited. Nitrogen gas fills nylon bag at 150-250 miles/hr

NaN₃ ? N₂ + Na

2. Reaction with potassium nitrate (1st stage to eliminating dangerous by-products)

Na + KNO₃ ? N₂ + Na₂O + K₂O

3. Reaction with sodium and potassium oxide to form silicate glass (2nd stage to eliminating dangerous by-products)

K₂O + SiO₂ ? K₄SiO₄ Na₂O + SiO₂ ? Na₄SiO₄

A typical 60L airbag requires 5.82 moles of nitrogen gas to fill it up. A manufacturer puts 65.0 g of SiO₂ in an airbag. Using stoichiometry, we are going to find out how many grams of SiO₂ is required to completely neutralize the dangerous by-products of the airbag reaction & conclude whether 65.0 g is enough.

PART A:

1. Use stoichiometry to calculate the number of moles of sodium produced by the first reaction if 378.3g of NaN₃ is used. SHOW ALL YOUR WORK & BE NEAT!! Use significant figures where appropriate.

NaN₃? N₂+Na

PART B:

2. Sodium is very reactive and must be neutralized. Using the number of moles of Na produced from the first reaction, calculate using stoichiometry. SHOW ALL YOUR WORK & BE NEAT!! Use significant figures where appropriate.

Na + KNO3 ? N2 + Na2O + K2O

2a) how many moles of Na2O are created?

2b) how many moles of K2O are created?

PART 3 ; SHOW ALL YOUR WORK AND BE NEAT.

The products Na₂O + K₂O are also dangerous, and must further be neutralized by SiO₂ to produce K₄SiO₄ and Na₄SiO₄

3a) What mass of SiO₂ would be required in order to fully react with all of the of K₂O from question (2)?

K₂O + SiO2 ? K₄SiO₄

3b) What mass of SiO₂ would be required in order to fully react with all of the of Na₂O from question (2)

Na2O + SiO2 ? Na₄SiO₄

4. How much SiO₂ is needed in total? Was 65 g of SiO₂ enough?

Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 p.m. with the meters off resulted in the following speeds (in miles per hour).

Does there appear to be a difference in the speeds?

A.Yes, the Meters Off data appear to have higher speeds.

B.Yes, the Meters On data appear to have higher speeds.

C.No, the box plots do not show any difference in speeds.

Are there any outliers?

A.Yes, there appears to be a high outlier in the Meters On data.

B.No, there does not appear to be any outliers.

C.Yes, there appears to be a low outlier in the Meters On data.

D.Yes, there appears to be a high outlier in the Meters Off data.

Are the ramp meters effective in maintaining a higher speed on the freeway? Use the alphaαequals=0.01 0.01 level of significance. State the null and alternative hypotheses. Choose the correct answer below.

Determine the P-value for this test.

Choose the correct conclusion

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.

State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

Determine the P-value for this hypothesis test.(round to 3 decimals)

State the appropriate conclusion. Choose the correct answer below.

The data is

Carpeted: 15.3,12.9,10.2,6.9,15.6,12.7,10.6,14.6

Uncarpeted;8.7,10,11.2,10.7,14,6.9,6.4,11.1

Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 p.m. with the meters off resulted in the following speeds (in miles per hour).

Does there appear to be a difference in the speeds?

A.Yes, the Meters Off data appear to have higher speeds.

B.Yes, the Meters On data appear to have higher speeds.

C.No, the box plots do not show any difference in speeds.

Are there any outliers?

A.Yes, there appears to be a high outlier in the Meters On data.

B.No, there does not appear to be any outliers.

C.Yes, there appears to be a low outlier in the Meters On data.

D.Yes, there appears to be a high outlier in the Meters Off data.

Are the ramp meters effective in maintaining a higher speed on the freeway? Use the alphaαequals=0.01 0.01 level of significance. State the null and alternative hypotheses. Choose the correct answer below.

Determine the P-value for this test.

Choose the correct conclusion

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.

State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

Determine the P-value for this hypothesis test.(round to 3 decimals)

State the appropriate conclusion. Choose the correct answer below.

The data is

Carpeted: 15.3,12.9,10.2,6.9,15.6,12.7,10.6,14.6

Uncarpeted;8.7,10,11.2,10.7,14,6.9,6.4,11.1

Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel.

(a-1) Comparison of GPA for randomly chosen college juniors and seniors:

x¯1x¯1 = 4.75, s₁ = .20, n₁ = 15, x¯2x¯2 = 5.18, s₂ = .30, n₂ = 15, α = .025, left-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

(a-2) Based on the above data choose the correct decision.

• Do not reject the null hypothesis

• Reject the null hypothesis

(b-1) Comparison of average commute miles for randomly chosen students at two community colleges:

x¯1x¯1 = 25, s₁ = 5, n₁ = 22, x¯2x¯2 = 33, s₂ = 7, n₂ = 19, α = .05, two-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)
  

(b-2) Based on the above data choose the correct decision.

• Reject the null hypothesis

• Do not reject the null hypothesis

(c-1) Comparison of credits at time of graduation for randomly chosen accounting and economics students:

x¯1x¯1 = 150, s₁ = 2.8, n₁ = 12, x¯2x¯2 = 143, s₂ = 2.7, n₂ = 17, α = .05, right-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

(c-2) Based on the above data choose the correct decision.

• Reject the null hypothesis

• Do not reject the null hypothesis

Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel.

(a-1) Comparison of GPA for randomly chosen college juniors and seniors:

x¯1x¯1 = 4.75, s₁ = .20, n₁ = 15, x¯2x¯2 = 5.18, s₂ = .30, n₂ = 15, α = .025, left-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

(a-2) Based on the above data choose the correct decision.
  

• Do not reject the null hypothesis

• Reject the null hypothesis

(b-1) Comparison of average commute miles for randomly chosen students at two community colleges:

x¯1x¯1 = 25, s₁ = 5, n₁ = 22, x¯2x¯2 = 33, s₂ = 7, n₂ = 19, α = .05, two-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)
  

(b-2) Based on the above data choose the correct decision.

• Reject the null hypothesis

• Do not reject the null hypothesis

(c-1) Comparison of credits at time of graduation for randomly chosen accounting and economics students:

x¯1x¯1 = 150, s₁ = 2.8, n₁ = 12, x¯2x¯2 = 143, s₂ = 2.7, n₂ = 17, α = .05, right-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

(c-2) Based on the above data choose the correct decision.
  

• Reject the null hypothesis

• Do not reject the null hypothesis