We discussed some of the theoretical aspects of the social discount rate (r) in class. The benchmark for cost-bene t analysis by the public sector was set by the O ce of Management & Budget (OMB) in 1992 to 7%. However, Obama's Council of Economic Advisers questioned this (see the policy paper posted under additional reading). In the 1970s, the OMB used 10%, and then lowered it in the 1980s to 8%. In the 1950s, the Army Corps of Engineers used a discount rate of 2.5%.

In 1965, the economist Kenneth Boulding testi ed before the Congressional Subcommittee on Irrigation & Reclamation and recited a poem regarding the issue:

The long-term interest rate
Determines any project's fate:
At 2 percent the case is clear,
At 3 percent some sneaking doubts appear, At 4 percent it draws its nal breath, While 5 percent is certain death.

4

Boulding's lyrics suggest that the discount rate (r) a ects whether a project will be approved that is, whether P V (B) > P V (C) or not. Answer the following questions about the discount rate and its a ects on cost-bene t calculations.

(a) Consider a project that costs $12 million initially, but then after 10 years (t = 10), it has a (one-time) bene t of $24 million. Use three of the above-mentioned discount factors 2.5%, 7%, and 10% to demonstrate Boulding's point. Under which discount factors would the project be approved?

(b) Since the costs of projects are typically incurred in the earlier years of a project (while the bene ts typically last into the future), how might an increase in the discount rate a ect NPV calculations? Demonstrate your reasoning using the project values in Table 2 and the three discount rates used in the previous question (2.5%, 7%, and 10%). How do the P V (B) and P V (C) change with over the three di erent discount rates?

Table 2: Project Costs and Benefits

(c) As noted in class, the bene t-cost B/C ratio is really the ratio (PV (B)/PV (C)). When it is greater than 1, NPV > 0. There is an easily deciphered relationship between the internal rate of return (IRR) and the B/C ratio when the PV(B) is a perpetuity. In the case where PV(B) is a perpetuity, the bene t amount (B) is constant each year and continues inde nitely. (It is used frequently in examples in the textbook.) The perpetuity formulation is P V (B) = (B/r). Since the IRR is the discount rate (r) that makes PV (B) = PV (C), we can say that the IRR is when

0 = (B/r)?PV(C) = (B/IRR)?PV(C)
What is the IRR for the project described by Table 2? What is the value of the B/C

ratio if the discount rate (r) is equal to the IRR?

Suppose you throw a ball into the air. Do you think it takes longer to reach its maximum height or to fall back to earth from its maximum height? We will solve the problem in this project, but before getting started, think about that situation and make a guess based on your physical intuition. 1. A ball with mass m is projected vertically upward from the earth’s surface with a positive initial velocity v0. We assume the forces acting on the ball are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude p|v(t)|, where p is a positive constant and v(t) is the velocity of the ball at time t. In both the ascent and the descent, the total force acting on the ball is pv mg. (During ascent, v(t) is positive and the resistance acts downward; during descent, v(t) is negative and the resistance acts upward.) So, by Newton’s Second Law, the equation of motion is mv0 = pv mg Solve this di↵erential equation to show that the velocity is v(t) = ✓ v0 + mg p ◆ ept/m mg p 2. Show that the height of the ball, until it hits the ground, is y(t) = ✓ v0 + mg p ◆ m p ⇣ 1 ept/m⌘ mgt p 3. Let t1 be the time that the ball takes to reach its maximum height. Show that t1 = m p ln ✓mg + pv0 mg ◆ Find this time for a ball with mass 1 kg and initial velocity 20 m/s. Assume the air resistance is 1 10 of the speed. 1 4. Let t2 be the time at which the ball falls back to earth. For the particular ball in Problem 3, estimate t2 by using a graph of the height function y(t). Which is faster, going up or coming down? 5. In general, it’s not east to find t2 because it’s impossible to solve the equation y(t)=0 explicitly. We can, however, use an indirect method to determine whether ascent or descent is faster: We determine whether y(2t1) is positive or negative. Show that y(2t1) = m2g p2 ✓ x 1 x 2 ln x ◆ where x = ept1/m. Then show that x > 1 and the function f(x) = x 1 x 2 ln x is increasing for x > 1. Use this result to decide whether y(2t1) is positive or negative. What can you conclude? Is ascent or descent faster?

Please answer #3

Please restate the problem to be solved, and define all variables and parameters. Please explain your reasoning and strategy for solving the problem. Please go over basic principals or key processes underlying the problem that was addressed in the paper. Please include an interpretation of the information in the context in which the problem was solved. Please state your conclusions in complete sentences which stand on their own

Sorry, I know this is a lot

1. Assume that a company has two cost drivers—number of courses and number of students. The planned number of courses and students were 5 and 100, respectively. The actual number of courses and students were 6 and 110, respectively. One of the company’s expenses is influenced by both cost drivers and it has a fixed element as well. Its cost formulas are $50 per course, $5 per student, and $1,000 per period. The total actual amount of this expense is $1,880. The spending variance for this expense would be:

a. 30 U

b. $30 F

c. $130 F

d. $130 U

2. Assume that a company provided the following cost formulas for three of its expenses (where q refers to the number of hours worked):

The company’s planned level of activity was 2,000 hours and its actual level of activity was 1,900 hours. If these are the company’s only three expenses, what total amount of expense would appear in the company’s flexible budget?

a. $12025

b. $12175

c. $12650

d. $12250

A professor has noticed that, even though attendance is not a component of the final grade for the class, students that attend regularly generally get better grades. In fact, 48% of those who come to class on a regular basis receive A's. Only 6% who do not attend regularly get A's. Overall, 60% of students attend regularly. Based on this class profile, suppose we are randomly selecting a single student from this class, and answer the questions below.

Hint #1: pretend that there are 1000 students in the class and use the values given in the problem to construct the appropriate contingency table. Round cell frequencies to the nearest integer

Hint #2: No joke, you really need to use hint #1.

Hint #3: The first step to using hint #1 is to calculate the totals for those who attend regularly and do not attend regularly.

A) P(receives A's | attends regularly) =

B) P(receives A's | does not attend regularly) =

C) P(receives A's) =

D) P(attends regularly | receives A's) =

E) P(does not attend regularly | does not receive A's) =

How fast can male college students run a mile? There’s lots of variation, of course. During World War II, physical training was required for male students in many colleges, as preparation for military service. That provided an opportunity to collect data on physical performance on a large scale. A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.01 minutes and standard deviation 0.7 minute.

It's good practice to draw a Normal curve on which this mean and standard deviation are correctly located. To do this, draw an unlabeled Normal curve, locate the points where the curvature changes (this is 1 standard deviation from the mean), then add number labels on the horizontal axis.

Use the Empirical Rule to answer the following questions.

1. What range of times covers the middle 99.7% of this distribution?
   
   From ______to _____minutes Round to 2 places.
   
2. What percent of these runners run the mile between 5.61 and 9.11 minutes?
   
   ______% Round to 2 places.
   
3. What percentage of the these running times are faster than 7.71 minutes?
   
   ________% Round to 2 places.

1. The average expenditure per student for a certain school year was $10337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10798. At α =0.01 level of significance, can it be concluded that the average expenditure has changed?

2. (10 pts) Suppose when you were visiting universities and deciding which to attend, the admission officers at Tennessee Wesleyan(TW) claimed TW students graduate in 4.25 years or less. You are now a student at TW and notice that a lot of students are graduating in more than 4.25 years. Therefore, you doubt that you were given accurate graduation rates by the TW admission officers. You collect data and compute graduation rates of TW graduates from the last 10 years (n=10). You obtain a mean graduation rate of 4.74 years and a standard deviation of 0.76 years. Do you have strong enough evidence to prove that TW admissions officers are not providing accurate rates at α =0.05 level of significance? Use hypothesis testing to determine your conclusion.

2-

The PACE project at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 (n = 334) and 21.2% in 2009 (n = 843). Test that the proportion of students reporting bingeing in 1999 is different from the proportion of students reporting bingeing in 2009 at the 10% significance level.

-A two-sided test with zcrit = -1.645 and 1.645.

-n 1 = n 1999 = 334

-n 2 = n 2009 = 843

-p ^ 1 = p ^ b i n g e 1999 = 0.422

-p ^ 2 = p ^ b i n g e 2009 = 0.212

A) Calculate the appropriate test statistic showing your work. What is the standard error?

B) What is the test statistic value?

C) Calculate the corresponding p-value from the appropriate table.

D) Construct a 90% confidence interval around the difference-in-proportions estimate. Lower bound and upper bound values?

For each exercise, answer the following along with any additional questions. Assume group variances are equal (unless the problem is ran via statistical software). |  Provide the null and alternative hypotheses in formal and plain language for appropriate two-tailed test (viz., dependent or independent) at the 0.05 significance level  Do the math and reject/accept null at a=.05. State your critical t value.  Explain the results in plain language.  Calculate the 95% confidence interval for the difference in means and state both formally and in plain language if appropriate.|

1. The State of Florida severely cut funding for the TRUTH campaign (advertising which is aimed at teenagers to reduce smoking). Advocates claim that TRUTH reduces teen smoking. To demonstrate this, they provide two separate samples of the state’s high school students reporting their number of cigarettes smoked per day two years before (nine students) and two years after the start of TRUTH (eight students). (C11PROB1.SAV) Before TRUTH: 5, 5, 8, 0, 0, 10, 0, 4, 10 After TRUTH: 6, 0, 6, 7, 0, 0, 2, 5

The PACE project at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 (n = 334) and 21.2% in 2009 (n = 843). Test that the proportion of students reporting bingeing in 1999 is different from the proportion of students reporting bingeing in 2009 at the 10% significance level.

-A two-sided test with zcrit = -1.645 and 1.645.

-n 1 = n 1999 = 334

-n 2 = n 2009 = 843

-p ^ 1 = p ^ b i n g e 1999 = 0.422

-p ^ 2 = p ^ b i n g e 2009 = 0.212

A) Calculate the appropriate test statistic showing your work. What is the standard error?

B) What is the test statistic value?

C) Calculate the corresponding p-value from the appropriate table.

D) Construct a 90% confidence interval around the difference-in-proportions estimate. Lower bound and upper bound values?

Question #5: Educational psychologists were interested in the impact the "Just Say No!" Program and contracts on drunk driving among males vs. female teenagers. With the cooperation of school officials, 16-year-old students were matched and randomly assigned to one of two groups, with equal numbers of males and females in each group. Group A participated in a "Just Say No!" program, which required a one-hour information session instead of P.E. for six weeks. Students were presented with written factual information, motivational lectures, guidance films, and assertiveness training. Students were also encouraged to sign a personal responsibility contract that stipulated that they would not drink and drive. Group B participated in regular P. E. classes for the six-week experimental period. Please answer the following questions and justify your answer.

(a) Identify the experimental design.

(b) What is the independent variable? Quasi-independent variable? What is the dependent variable?

(c) Diagram this experimental design.

(d) State at least one potential confounding variable?

(e) How many main effects, interaction effects, simple main effects of A, and simple main effects of B are there?