Consider a casino game that an individual (Joe) wants to play. It costs him N dollars each time to play. He loves this game and wants to continue playing until he is either broke or he breaks the bank (wins all the money). The probability of winning is p; the probability of losing is q. These are fixed probability values every time the game is played.

Joe brought $M to the casino. Every time one plays you either lose the entrance fee ($N) or you win and are paid back D dollars.

(a) How much money does Joe expect to have after playing n times? Derive a formula for how much money he has.

(b) Suppose Joe starts with $100, p=0.3, q=0.7, N=$5, and D=$20. Is it likely that Joe will break the bank?

(c) If the answer to (b) is no, how many times is it likely that Joe can play this game before he is broke?

Below is a set of data collected

at 0.95 atm

for the formation of CO

2

gas produced when calcium

carbonate is reacted with aqueous HCl:

Time (min)

Volume CO

2

(mL)

1

0.2

0

2

0.3

0

3

0.5

0

4

0.7

0

5

0.9

0

6

1

.00

7

1.2

0

8

1.3

0

9

1.5

0

10

1.7

0

11

1.9

0

12

2

.00

13

2.2

0

14

2.4

0

15

2.5

0

16

2.7

0

17

2.9

0

18

3

.00

19

3.2

0

20

3.4

0

Your assignment is as follows:

1. Create a spreadsheet in Excel (or equivalent) that

contains this data and does the following

calculations

automatically:

a. Converts each gas volume measurement to

moles of CO

2

produced

(Use a

PV = nRT to

solve

). Do this twice: one column for 0

Assume that you are planning to have a party at your house. You really would like to have the party outside in the sun, but there is a chance that it might rain. You have two decisions to make – whether or not you will watch the forecast and then whether to have the party inside or outside. If you choose to watch the forecast, it will either tell you that the weather will be sunny or that it will be rainy. If you choose to watch the forecast, you will not have to make the location decision until after you see the forecast. If you do not watch the forecast, you do not get to know what the forecast would have said had you watched it – you need to make the location decision without the knowledge of the forecast. However, the forecast is imperfect (probabilities are below). It also costs you some time, and you are already cutting it close in terms of getting ready.

Your task is to draw the decision tree for this situation, answer some questions about the decision tree, and recommend a course of action on the basis if your analysis.

The information you will need:

Probabilities (note that p(A|B) signifies the probability of event A given that event B has occurred – it is a conditional probability).

p(forecast says it will be sunny) = 0.95

p(it is sunny|forecast said it would be sunny) = 0.99

p(it is sunny|forecast said it would be rainy) = 0.15

p(sunny) = 0.948 [hint: this is to use on the branch of the tree where you decide not to watch the forecast]

Utilities (note that U(case X) represents the utility of case X)

U(watch forecast, party indoors, sunny weather) = 0.3

U(watch forecast, party indoors, rainy weather) = 0.4

U(watch forecast, outdoors, sunny weather) = 0.9

U(watch forecast, outdoors, rainy weather) = 0.0

U(do not watch forecast, indoors, sunny weather) = 0.4

U(do not watch forecast, indoors, rainy weather) = 0.5

U(do not watch forecast, outdoors, sunny weather) = 1.0

U(do not watch forecast, outdoors, rainy weather) = 0.1

(a) (10 points): Draw the decision tree for this problem. Include clear labels for all branches. Include all probabilities and utilities.

(b) (10 points): If you choose to watch the forecast and it says that the weather will be sunny, should you have the party indoors or outdoors? What is your expected utility for this choice?

(c) (5 points): What should your sequence of decisions be? In other words, should you watch the forecast? If you do watch the forecast, what is the optimal location decision for each of the two possible forecast reports? What is your expected utility for the overall decision situation?

d) (10 points): Analyzing a simple party problem might seem silly. However, the structure of this tree has many important applications in engineering. Think of a project management situation that could be described by this structure of decision tree. Write a one-paragraph description of the decision situation you think of (like the description at the beginning of this question), and re-draw the tree with new labels on the branches. You do not need to include any probabilities or utilities on your new tree.

Dan and Cheryl are married, file a joint return, and have no children. Dan is a pharmaceutical salesman and Cheryl is a nurse at a local hospital. Dan's SSN is 400-20-1000 and Cheryl's SSN is 200-40-8000 and they reside at 2033 Palmetto Drive, Nashville, TN 28034. Dan is paid according to commissions from sales; however, his compensation is subject to withholding of income and payroll taxes. He also maintains an office in his home as the pharmaceutical company does not have an office in Nashville and when he is not traveling, Dan operates his business from his home office. During 2018, Dan earned total compensation from his job of $125,000, on which $18,000 of federal income taxes were withheld, $7,750 of OASDI, and $1,813 of Medicare taxes. State income taxes of $4,000 were withheld. Cheryl earned a salary during 2016 of $45,400, on which federal taxes withheld were $4,000, OASDI of $2,815, and Medicare taxes of $658.

During 2017, Dan and Cheryl had interest income from corporate bonds and bank accounts of $1,450 and qualified dividends from stocks of $5,950. Dan also actively trades stocks and had the following results for 2017:

LTCG $4,900

LTCL ($3,200)

STCG $0

STCL ($7,800)

He had no capital loss carryovers from previous years. Dan does a considerable amount of travel in connection with his job. He uses his own car and is reimbursed $0.30 per business mile. During 2018, Dan drove his car a total of 38,000 miles (evenly throughout the year), of which 32,000 were business related. He also had business-related parking fees and tolls during the year of $280. Dan uses the mileage method for deducting auto expenses. Dan also had the following travel expenses while away from home during the year: Hotel $4,200

Meals $820

Entertainment of customers $1,080

Tips $100

Laundry and cleaning $150

Total $6,350

Dan was reimbursed for the travel expenses by his employer, pursuant to an accountable plan, in the amount of $5,080.
Dan's expenses in connection with his office in the home were as follows:

Office supplies $ 290

Telephone (separate line) $1,100

Utilities (entire house) $3,400

Homeowners insurance $600

Interest and property taxes (see below for totals)

Repairs and maintenance (entire house) $800

Dan's office is 300 square feet and the total square footage of the house is 3,000 square feet. Dan and Cheryl purchased the house on June 12, 2007, for $280,000, of which $40,000 is attributable to the land.

Cheryl incurred several expenses in connection with her nursing job. She paid $450 in professional dues, $200 in professional journals, and $350 for uniforms. Dan and Cheryl had the following other expenditures during the year:

Health insurance premiums (after-tax) $ 4,400

Doctor bills $470

Real estate taxes on home $2,200

Personal property taxes $400

Mortgage interest $15,600

Charitable contributions cash $9,000

Charitable contributions GE stock owned for 5 years: FMV $8,000 Adjusted basis $2,000

Tax preparation fees $750

Please fill out Form 1040 with Schedule 1 and 4 as well as Schedule A,C,D, and SE. Also Form 8829 for 2018

Thank you

Dan and Cheryl are married, file a joint return, and have no children. Dan is a pharmaceutical salesman and Cheryl is a nurse at a local hospital. Dan's SSN is 400-20-1000 and Cheryl's SSN is 200-40-8000 and they reside at 2033 Palmetto Drive, Nashville, TN 28034. Dan is paid according to commissions from sales; however, his compensation is subject to withholding of income and payroll taxes. He also maintains an office in his home as the pharmaceutical company does not have an office in Nashville and when he is not traveling, Dan operates his business from his home office. During 2017, Dan earned total compensation from his job of $125,000, on which $18,000 of federal income taxes were withheld, $7,750 of OASDI, and $1,813 of Medicare taxes. State income taxes of $4,000 were withheld. Cheryl earned a salary during 2016 of $45,400, on which federal taxes withheld were $4,000, OASDI of $2,815, and Medicare taxes of $658.

During 2017, Dan and Cheryl had interest income from corporate bonds and bank accounts of $1,450 and qualified dividends from stocks of $5,950. Dan also actively trades stocks and had the following results for 2017:

LTCG $4,900

LTCL ($3,200)

STCG $0

STCL ($7,800)

He had no capital loss carryovers from previous years. Dan does a considerable amount of travel in connection with his job. He uses his own car and is reimbursed $0.30 per business mile. During 2017, Dan drove his car a total of 38,000 miles (evenly throughout the year), of which 32,000 were business related. He also had business-related parking fees and tolls during the year of $280. Dan uses the mileage method for deducting auto expenses. Dan also had the following travel expenses while away from home during the year: Hotel $4,200

Meals $820

Entertainment of customers $1,080

Tips $100

Laundry and cleaning $150

Total $6,350

Dan was reimbursed for the travel expenses by his employer, pursuant to an accountable plan, in the amount of $5,080.
Dan's expenses in connection with his office in the home were as follows:

Office supplies $ 290

Telephone (separate line) $1,100

Utilities (entire house) $3,400

Homeowners insurance $600

Interest and property taxes (see below for totals)

Repairs and maintenance (entire house) $800

Dan's office is 300 square feet and the total square footage of the house is 3,000 square feet. Dan and Cheryl purchased the house on June 12, 2007, for $280,000, of which $40,000 is attributable to the land.

Cheryl incurred several expenses in connection with her nursing job. She paid $450 in professional dues, $200 in professional journals, and $350 for uniforms. Dan and Cheryl had the following other expenditures during the year:

Health insurance premiums (after-tax) $ 4,400

Doctor bills $470

Real estate taxes on home $2,200

Personal property taxes $400

Mortgage interest $15,600

Charitable contributions cash $9,000

Charitable contributions GE stock owned for 5 years: FMV $8,000 Adjusted basis $2,000

Tax preparation fees $750

Compute Dan and Cheryl's income tax liability for 2017. Disregard the alternative minimum tax.

1.

USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 996 Chevrolet owners and found that 503 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to the car company is more than 47%? Use α = 0.01. Solve the problem using both the traditional method and the P-value method. Since the sampling distribution of p̂ is the normal distribution, you can use critical values from the standard normal distribution as shown in the table of critical values of the z distribution. (Round the test statistic and the critical value to two decimal places. Round the P-value to four decimal places.)

State your conclusion in context of the application.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of consumers loyal to the car company is more than 47%.

There is insufficient evidence at the 0.01 level to conclude that the true proportion of consumers loyal to the car company is more than 47%.     

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

The conclusions obtained by using both methods are the same.

We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.  

   We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.

2.

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. Solve the problem using the critical region method of testing. (Let d = January − April. Round your answers to three decimal places.)

Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.

Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.    

Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January.

Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January.

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

We reject the null hypothesis using the critical region method, but fail to reject using the P-value method.

We reject the null hypothesis using the P-value method, but fail to reject using the critical region method.     

The conclusions obtained by using both methods are the same.

1. Tom is a civil engineer and working in a large construction project. Tom was assigned by his manager to look for steel suppliers for the project. Tom placed a newspaper advertisement for potential suppliers to bid. A potential supplier approached Tom, indirectly requested Tom to buy steel from his company. Then he invited Tom to an expensive dinner and a boat tour. Tom was planning to accept the dinner invitation and boat tour. (a) Identify the ethical situation in this case (if any) (b) Explain what Tom should do (c) Mention the relevant Rule of Practice or Professional Obligation (if any)

2. Nathan and Bill are electrical engineers. They are colleagues and working for a reputed private firm. One day Nathan saw that his colleague Bill is accepting a new laptop as a gift from a material supplier. Next day, Nathan talked with Bill about this and told him that this is not appropriate. Bill did not care. After a couple of months later, Nathan got to know that the same supplier has arranged a vacation (i.e., air ticket, hotel etc.) in Hawaii for Bill. (d) Identify the ethical situation in this case (if any) (e) Explain what Nathan should do (f) Mention the relevant Rule of Practice or Professional Obligation (if any)

Betty, the chief nursing officer, had to make a decision about buying 120 new hospital beds for patient rooms. After she interviewed nurse mangers at the units where the beds were going to be placed, Betty compiled her findings and decided to contact a well-known equipment company to obtain prices and contracts. The equipment company’s executive salesperson, Jim, discussed options at length with her and invited her and her significant other to an upcoming all-expenses-paid lavish retreat at a five-star hotel in Hawaii to see demonstrations of the beds and to hear a comprehensive sales pitch. Betty thought to herself, “We badly need some relaxation and stress relief. Hawaii would be so much fun. Would it be wrong for us to go?”

If you were Betty, what would you do? Give your rationale. Justify your answer with an ethical framework—a theory, approach, or principle.

Do you consider this situation a conflict of interest? Why or why not? Give your rationale.

What policies, if any, should be in place regarding a scenario such as this one? Do you have any such policies in place at work for similar situations? Do such policies impact day-to-day activities in any way?