Mr Lim is a tuition teacher. He is deciding how many hours to teach each day and how much to charge for his tuition. Each hour of lecture leaves him fatigued, which is equivalent to a cost of $40 per hour to him. He has two students A and B with demand curves as follows:

Student A: PA= 72 - 8Q

Student B: PB = 56 - 4Q where Q is the number of hours he teaches.

(i) If he can teach only one student per hour, obtain the market demand curve for his tuition from the two students. If he wishes to maximise social welfare, how many hours of tuition should he teach? Discuss.

(ii) Suppose that he can broadcast his tuition online, so that both students can listen to his tuition at the same time and consumption is nonrivalrous. Obtain the market demand curve. What is the socially optimal number of hours of tuition he should provide? Discuss.

2018-Jan Q4b

A guidance counselor claims that high school students in a college preparation program have higher ACT scores than those in a general program. The sample mean ACT score for 49 high school students who are in a college preparation program is 22.2 and the sample standard deviation is 4.8. The sample mean ACT score for 44 high school students who are in a general program is 20.0 and the sample standard deviation is 5.4.  

Use an 8% level of significance to conduct test the guidance counselor’s claim. Assume the distribution of ACT scores for both programs are approximately normally distributed. Assume that σ_{college prep}² ‡ σ_general² .  

H₀:                                                                                      Level of significance (α):   α =         

H_A:                                                                                     Type test:     two-tailed    left tail      right tail

Specify the random variable and distribution to be used in this hypothesis test.

Calculate the p-value                                                          Draw a graph and show the p-value

Show your work and any calculator functions used.

Compare the p-value with α                             Decide to Reject or Fail to reject the null hypothesis                   

Conclusion. State your results in non-technical terms.

10. In a study conducted to determine whether the role that sleep disorders play in academic performance, researcher conducted a survey of 1800 college students to determine if they had a sleep disorder. Of the 500 students with a sleep disorder, the mean GPA was 2.51 with a standard deviation of 0.85. Of the 1300 students without a sleep disorder, the mean GPA is 2.85 with a standard deviation of 0.78. Test the claim that sleep disorder adversely affects one’s GPA at the 0.05 level of significance?

11. In one experiment, the participant must press a key on seeming a blue screen and reaction time (in seconds) to press the key is measured. The same person is then asked to press a key on seeing a red screen, again with reaction time measured. The results for six randomly sampled study participants are as follows:

Participant

1

2

3

4

5

6

Blue

0.582

0.481

0.841

0.267

0.685

0.450

Red

0.408

0.407

0.542

0.402

0.456

0.522

Construct a 99% confidence interval about the population mean difference. Assume the differences are approximately normally distributed.

Problem 4. Consider a simple solar system that contains one star (mass M) and one planet (mass m) in a circular orbit with radius r. The planet orbits at speed v. (v can be computed in terms of G, M, m, and r using Kepler’s 3rd Law and/or Newton’s Law of Gravitation.) Due to conservation of momentum, as the planet changes its velocity vector, the star’s velocity vector will also change. Astronomers can detect a star’s changing velocity from its spectral lines and infer the presence of a planet. (This is called the ‘radial velocity’ method for exoplanet detection.) (a) What is the difference in the planet’s momentum, ∆~p, from one point on its orbit to the opposite point? Assume that the planet moves in the ±x-direction at these two points. You can leave your answer in terms of v, the orbital speed of the planet. (b) Briefly explain why the momentum of the planet is not constant, but the momentum of the star plus the momentum of the planet IS constant. (c) Relative to v, what is the maximum speed of the star during the orbit of the planet? Assume we are in the ‘center of momentum’ frame of reference, where the total momentum of the system is zero. (d) Plug in numbers to find the speed of our Sun induced by the orbit of Earth. (This is a bit artificial, since Jupiter has a much bigger effect, but just to get a sense of the size of the numbers. . . ) The Sun has MSun = 2 × 1030 kg, and Earth has mEarth = 6 × 1024 kg and orbits at r = 1 AU = 1.5 × 1011 m. (e) Plug in numbers to find the speed of the star Gliese 581 induced by the orbit of its planet, Gliese 581 e, which is the least massive exoplanet detected so far using the radial velocity method. Gliese 581 has M = 0.31MSun, and Gliese 581 e has m = 2.5mEarth and orbits at r = 0.028 AU. (f) We detected Gliese 581 e by measuring its star’s change in velocity; could (hypothetical) alien astronomers on Gliese 581 e plausibly detect Earth using the same method and same equipment?

6.1 A statute gives the Department of the Interior the power to allow or to curtail mining within the national forests “as the best interests of all users of the national forest shall dictate.” Is this a valid delegation of legislative power to the agency, or is it too broad a delegation of power? 8.1 Before deciding which remedies are available under Article 2 of the UCC, one must first determine whether the transaction involved the sale of goods. Consider the following fact patterns. A. Tanzer entered into a contract with Audio Visual Artistry to install a “smart home” system in Tanzer’s house, which was under construction. The contract included expert installation services for a custom home theatre, lighting, music, and phone system. Was the contract for a sale of goods or services? [Audio Visual Artistry v. Tanzer, 403 S.W.3d 789 (Tenn. Ct. App. 2012).] B. Wachter, a construction company, entered into a contract to purchase an accounting and project management software package from DCI, a company that develops, markets, and supports software for construction companies. The package included “installation of the software, a full year of maintenance, and a training and consulting package.” Was the contract for a sale of goods or services? [Wachter Management Co. v. Dexter & Chaney, Inc., 144 P.3d 747 (Kan. 2006).] C. A customer sued a New York restaurant for breach of warranty after a glass of water allegedly exploded in his hand during the course of a meal. Does the claim involve the sale of goods? [Gunning ex rel. Gunning v. Small Feast Caterers, Inc., 777 N.Y.S.2d 268 (N.Y. Sup. 2004).] D . Brenda Brandt underwent an operation at the Sarah Bush Lincoln Health Center to implant a ProtoGen Sling to resolve her urinary incontinence. Instead of solving the problem, the sling resulted in serious complications and was subsequently removed. After the device was recalled by its manufacturer, Brandt sued the Health Center for breach of warranty. Does the claim involve the sale of goods or services? [Brandt v. Boston Scientific Corp., 792 N.E.2d 296 (Ill. 2003).

Spousal Consent

Provisions of the Florida Therapeutic Abortion Act, which required a married woman to obtain the husband’s consent before abortion, were found to be unconstitutional. The state’s interest was found not to be sufficiently compelling to limit a woman’s right to abortion. The husband’s interest in the baby was held to be insufficient to force his wife to face the mental and physical risks of pregnancy and childbirth.43 In Doe v. Zimmerman (1975),44 the court declared unconstitutional the provisions of the Pennsylvania Abortion Control Act, which required that the written consent of the husband of a married woman be secured before performing an abortion. The court found that these provisions impermissibly permitted the husband to withhold his consent either because of his interest in the potential life of the fetus or for capricious reasons. The natural father of an unborn fetus in Doe v. Smith (1988)45 was not entitled to an injunction to prevent the mother from submitting to an abortion. Although the father’s interest in the fetus was legitimate, it did not outweigh the mother’s constitutionally protected right to an abortion, particularly in light of evidence that the mother and father had never married. In the 1992 decision of Planned Parenthood v. Casey, the Supreme Court ruled that spousal consent would be an undue burden on the woman.

Incompetent Persons’ Consent

Abortion was found to be proper by a family court in In re Doe (1987)46 for a profoundly retarded woman. She had become pregnant during her residence in a group home as a result of a sexual attack by an unknown person. The record had supported a finding that if the woman had been able to do so she would have requested the abortion. The court properly chose welfare agencies and the woman’s guardian ad litem (a guardian appointed to prosecute or defend a suit on behalf of a party incapacitated by infancy, mental incompetence, etc.) as the surrogate decision makers.

The Court Was Appalled, Tomcik v. Ohio Dep’t of Rehabilitation and Correction.

In 500 words explain the following

1. Do you agree with the court’s decision? Discuss your answer

2. Discuss why the court was appalled

3. What ethical values were lacking by the caregivers?

Background Information: Rights of Grandparents

As family structures have changed due to increases in divorce and single parenting, the role of grandparents has also changed. As a result, more decisions about grandparents’ visitation rights are being made by courts and state legislatures. Since the mid-1970s, all 50 states have passed laws granting grandparents the right to petition the courts for legally enforced visitation privileges. Before this time period, grandparents had no rights to their grandchildren except by consent of the children’s parents.

Early court decisions (e.g., Odell v. Lutz, 1947) emphasized parental autonomy and ruled that grandparent visitation rights would undermine parental authority. In fact, it was stated that grandparent visitation rights could subject children to intergenerational conflict (e.g., Noll v. Noll, 1950). These rulings also went along with the long tradition that the legal system should only intervene in the family in extreme circumstances. Early granting of grandparent visitation rights (e.g., Benner v. Benner, 1952) came in cases in which the grandchildren had lived with the grandparents for extended periods, or in cases in which the parents were deemed “unfit,” and the grandparents were given custody.

Consider the landmark case of Troxel v. Granville (2000). In 2000, based on this case, the United States Supreme Court placed limits on the grandparent visitation laws. The court concluded that parents who provide adequate care for their children must be able to decide with whom their children will associate. To leave such decisions up to a judge, in the view of the Supreme Court, would conflict with parents’ basic constitutional rights.

Discussion Question:

Discuss the pros and cons of regulated and enforced grandparent visitation rights. Part of your answer and discussion should involve the roles that grandparents play in grandchildren’s lives (e.g., alternative caregivers, playmates, family historians and transmitters of family values and traditions, advice-givers to parents). Also consider how to resolve intergenerational conflict, how to determine the “children’s best interests,” the consequences of grandparent visitation rights on family functioning, and how to resolve the grandparent policy.

Alumni donations are an important source of revenue for college and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student-faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. Table 15.13 shows data for 48 national universities (America’s Best Colleges, Year 2000 Edition). The column labeled Graduation Rate is the percentage of students who initially enrolled at the university and graduated. The column labeled % of Classes Under 20 shows the percentage of classes offered with fewer than 20 students. The column labeled Student-Faculty Ratio is the number of students enrolled divided by the total number of faculty. Finally, the column labeled alumni Giving Rate is the percentage of alumni that made a donation to the university.

Acquisitions and Payment Cycles

• List the accounts which are significant in acquisitions and payment cycles.

• List why these accounts are considered significant and how they are involved in the acquisition and payment cycle.