1. Given a randomly chosen 4-digit number...

What is the probability...

a. That there are no pairs of consecutive digits in the number

b. That there are no pairs of consecutive digits in the number, if the last digit and first digit of the number could be classified as consecutive

c. Given a randomly chosen six digit number:

What is the probability that the number is an odd number if it contains the six digits 7-6-4-4-3-1, and is in a random order?

For Questions 1-4 , use the table below. It is data for the heights (inches) for Ms. Smith’s 4^th grade class.

1. The median height of the students is
   1. 42.32
   2. 52.50
   3. 54.45
   4. 58.35

2. The standard deviation (assume sample) of the students is
   1. 9.51
   2. 12.32
   3. 43.54
   4. 55.25

3. What is the z-score for the student who is 91 inches tall?
   1. Cannot be calculated from the data provided
   2. 0.00
   3. -3.76
   4. 3.76

4. Which measurement of central tendency is the best choice to describe the height of the students?
   1. Mode
   2. Median
   3. Mean
   4. Weighted Mean

1. What is the circular flow of income? What are the 4 key markets of the circular flow model?

2. Why is the aggregate demand curve for goods & services inversely related to the price

level? What does this inverse relationship indicate?

3. Why does the short-run aggregate supply (SRAS) curve slope upward to the right? What

does the upward slope indicate?

4. What are the major factors that influence the quantity of goods & services a group of

people can produce in the long run? Why is the long run aggregate supply curve (LRAS)

vertical? What does the vertical nature of the curve indicate?

5. If the price level in the current period is higher than what buyers and sellers anticipated,

what will tend to happen to real wages and the level of employment? How will the profit

margins of business firms be affected? How will the actual rate of unemployment compare

with the natural rate of unemployment? Will the current rate of output be sustainable in

the future?

6. Why is an unanticipated increase in the price level likely to expand output in the short run,

but not in the long run?

1–4 PART A - PLAN

The situation is as follows: With the cost of attendance rising, BYU administrators are worried that BYU students are graduating with more and more debt. In a random sample of 312 BYU undergraduate students who graduated in April 2019, 145 of them reported having student debt. Is there sufficient evidence to conclude that less than half of BYU undergraduate students who graduated in April 2019 have student debt? Use a 5% significance level. SHOW YOUR WORK IN ALL THE STEPS. ANSWERS WITHOUT SOLUTIONS WILL ONLY GET PARTIAL CREDIT.

As an example, if you were to take the square root of (2+2) / 3, please write it as sqrt((2+2)/3) when showing work.

1. State the name of the appropriate test procedure you will use (e.g., one-sample t test for means). (1pt)

2. Describe the parameter of interest in the context of the problem. (1 pt)

3. State the null and alternative hypotheses. (2 pts)

4. Write down the significance level. (1 pt.)

5. List and check the conditions for the test procedure you named above. (4 pts)

6. Obtain the value of the sample proportion (Round your answer to FOUR decimal places). Show your work. (1 pt)

7. Write the calculated test statistic (including your calculations) and its associated p-value using the appropriate table, not from statistical software. Round your final answer for the test statistic to two decimal places. Show formula and calculations. (2 pts)

8. Answer the question posed in the STATE step in context. Do this by including these three parts in your conclusion (3 pts): Compare p-value with α Decide whether to reject or fail to reject the null hypothesis State your conclusion in context.

Part B

The situation is as follows: With the cost of attendance rising, BYU administrators are worried that BYU students are graduating with more and more debt. In a random sample of 312 BYU undergraduate students who graduated in April 2019, 145 of them reported having student debt. Calculate a 98% confidence interval estimate for the proportion of BYU undergraduate students who graduated in April 2019 who have student debt. SHOW YOUR WORK IN ALL THE STEPS. ANSWERS WITHOUT SOLUTIONS WILL ONLY GET PARTIAL CREDIT.

As an example, if you were to take the square root of (2+2) / 3, please write it as sqrt((2+2)/3) when showing work.

9. State the name of the appropriate estimation procedure (e.g. one-sample t confidence interval for estimating the mean difference). (1 pt) (Note) You have already described the parameter being estimated in part A, so you don't have to repeat it here.

10. You have already listed the conditions, now check the condition for the normality of the sampling distribution of p-hat for confidence interval estimation. (1 pt.)

11. Write down the confidence level and the z* critical value. (2 pts.)

12. Calculate the confidence interval in interval form. Be sure to show your work. Round your final answer for the lower and upper limits to three decimal places. (2 pts)

13. Interpret your confidence interval in context. Do this by including these three parts in your conclusion (3 pts): Level of confidence Parameter of interest in context The interval estimate

4. Suppose that the supply of bourbon (unit = 1 bottle) is given by P = Q. The (inverse) demand for the product is given by P = 200 – 4Q. Suppose the government introduces a tax on bourbon of $15 per bottle, to be paid to the government by consumers.

a. What is the market quantity and price before the tax goes into effect?

b. What is the new market price and quantity after the tax goes into effect?

c. How much of the tax do the consumers bear? How much do suppliers bear?

d. Who bears the larger burden of this tax? Why?

e. What is the deadweight loss associated with this $15 tax on each bottle of bourbon?

f. Now suppose the government decides to impose the tax on suppliers instead of consumers. How would this affect your answers to (b), (c), (d), and/or (e)?

A mass m = 1 kg is attached to a spring with constant k = 4 N/m and a dashpot with variable damping coefficient c. If the mass is to be pulled 5 m beyond its equilibrium (stretching the spring) and released with zero velocity, what value of c ensures that the mass will pass through the equilibrium position and compress the spring exactly 1 m before reversing direction?

c =

1. Here is the demand for coconuts:

P            3          4            5        6         7          8         9          10         11         12          13

Q_D          1100      1000      900      800      700      600      500        400        300        200        100

And here is supply

P            3          4         5        6          7        8           9          10     11      12          13

Q_S           100        200        300        400        500        600        700        800        900        1000       1100

Identify the equilibrium price, quantity, consumer and producer surplus and show them on a graph. The graph should be pretty simple here, the main issue is finding the numbers for consumer and producer surplus. Again, let me reiterate: I WANT NUMBERS FOR CONSUMER AND PRODUCER SURPLUS! Furthermore, I want you to do this the way that I do (in other words, calculate it like it's a bunch of rectangles. Don't do the triangle thing that they do in the videos. Also, when doing this keep in mind that the width of these rectangles will not be 1 so be careful. (What is it? )

2. Which do you think is more elastic: demand for coffee or demand for Starbucks coffee? Show the demand for both. (Make sure to say which one is more elastic, so I know that you know.)

In each of problems 1 through 4: (a) Find approximate values of the solution of the given initialvalue problem at t=0.1, 0.2, 0.3, and 0.4 using the Euler methodwith h=0.1 (b) Repeat part (a) with h=0.05. Compare the results with thosefound in (a) (c) Repeat part (a) with h=0.025. Compare the results with thosefound in (a) and (b). (d) Find the solution y=φ(t) of the given problem and evaluateφ(t) at t=0.1, 0.2, 0.3, and 0.4. Compare these values with the results of (a), (b), and (c). 3. dy/dt = 0.5 -t +2y, y(0) = 1 Please also provide solution using Matlab.

1.      A company anticipates a depreciation deduction of $70,000 in year 4 of a project. The company's tax rate is 40% and its discount rate is 12%. The present value of the depreciation tax shield resulting from this deduction is closest to:

          A)     $17,808

          B)     $29,000

          C)     $21,000

          D)     $13,356

2.      (Ignore income taxes in this problem.) Nevland Corporation is considering the purchase of a machine that would cost $120,000 and would last for 6 years. At the end of 6 years, the machine would have a salvage value of $18,000. By reducing labor and other operating costs, the machine would provide annual cost savings of $43,000. The company requires a minimum pretax return of 19% on all investment projects. The net present value of the proposed project is closest to:

          A)     $32,966

          B)     $26,376

          C)     $64,902

          D)     $30,040

3.      (Ignore income taxes in this problem) The management of Elamin Corporation is considering the purchase of a machine that would cost $305,745 and would have a useful life of 9 years. The machine would have no salvage value. The machine would reduce labor and other operating costs by $51,000 per year. The internal rate of return on the investment in the new machine is closest to:

          A)     9%

          B)     11%

          C)     12%

          D)     10%

4.      (Ignore income taxes in this problem.) The management of Solar Corporation is considering the following three investment projects:

          Rank the projects according to the profitability index, from most profitable to least profitable.

          A)     M,N,L

          B)     L,N,M

          C)     N,L,M

          D)     N,M,L

5.      (Ignore income taxes in this problem.) The management of Lanzilotta Corporation is considering a project that would require an investment of $368,600 and would last for 8 years. The annual net operating income from the project would be $66,000, which includes depreciation of $31,000. The scrap value of the project's assets at the end of the project would be $15,000. The payback period of the project is closest to:

          A)     3.8 years

          B)     2.6 years

          C)     2.7 years

          D)     4.0 years

6.      Dunn Construction, Inc., has a large crane that cost $35,000 when purchased ten years ago. Depreciation taken to date totals $25,000. The crane can be sold now for $8,000. Assuming a tax rate of 40%, if the crane is sold the total after-tax cash inflow for capital budgeting purposes will be:

          A)     $7,400

          B)     $10,000

          C)     $8,800

          D)     $8,000

Question 4

A machine was acquired on January 1, 2015, at a cost of $80,000. The machine was originally estimated to have a residual value of $5,000 and an estimated life of 5 years. The machine is expected to produce a total of 100,000 components during its life, as follows: 15,000 in 2015, 20,000 in 2016, 20,000 in 2017, 30,000 in 2018, and 15,000 in 2019.

Instructions

(a)   Calculate the amount of depreciation to be charged each year, using each of the following methods:

       1.    Straight-line method

       2.    Units-of-production

       3.    Double diminishing-balance

(b)   Which method results in the highest depreciation expense during the first two years? Over all five years?

please answer this in microsoft word