Create one Excel file to submit named "Exam 3 Team X.xlsx" where X is your team letter.

Show work for credit. USE EXCEL

1. Use the data below.

a. Create a scatter plot. Say what you see.

b.  Use the data to develop an estimated regression equation showing how your team data is related to DOW, the Dow Jones industrial average. What is the estimated regression model (y-mx+b, slope & intercept)?
Let x represent the DOW indexes.

c.  How much of the variation in the sample values of your team data does the model estimated in part (b) explain?
Round your answer to two decimal places.

d. Suppose that the closing price for the DOW is 29,000. Estimate the closing price for your data

e. Preform a hypothesis test for the model (F test) with an significance of 0.05. State your conclusion.

f. Preform a hypothesis test for each of the estimated coefficients at the 0.05 level of significance. State your conclusions.

2. From the data above create 3 variables where Month01=1, 0 otherwise for Janurary, Month02=1, 0 otherwise for February, Month03=1, 0 otherwise for March.

a..  Use the data to develop an estimated regression equation showing how your team data is related to DOW, the Dow Jones industrial average. What is the estimated regression model?
Let x represent the DOW indexes.

b.  How much of the variation in the sample values of your team data does the model estimated in part (b) explain?
Round your answer to two decimal places.

c. Suppose that the closing price for the DOW is 29,000. Estimate the closing price for your data for April.

d. Preform a hypothesis test for the model (F test) with an significance of 0.05. State your conclusion.

e. Preform a hypothesis test for each of the estimated coefficients at the 0.05 level of significance. State your conclusions.

3. Use the data below

a.  Show the naive forecast, an exponential smoothing forecasts using α = 0.2, and a 3-month moving average forecast.

b. Compare the MFE, MSE, and MAPE on the models

c.  Make a conclusion on which model to use.

d. Find the alpha (smoothing constant) that minimizes the MSE.

Software analysis of the salaries of a random sample of

251

teachers in a particular state produced the confidence interval shown below. Determine if the following conclusions are correct. If​ not, state what is wrong with the conclusion. Complete parts a through e below.

​t-interval for

mu

​:

with

99

​%

​confidence,

43623

less thanmu​(TchPay)less than45465

​a) If many random samples of

251

teachers from this state were​ taken, about

99

out of

100

of them would produce this confidence interval.

Choose the correct answer below.

A.

This conclusion is​ correct, assuming all assumptions and conditions are met.

B.

This conclusion is incorrect. About

99

out of

100

intervals will produce a confidence interval that overlaps with this interval.

C.

This conclusion is incorrect. About

99

out of

100

intervals based on samples of any size would produce this confidence interval.

D.

This conclusion is incorrect. About

99

out of

100

intervals will contain the true mean​ salary, but different samples of

251

teachers will produce different confidence intervals.

​b) If many random samples of teachers from this state were​ taken, about

99

out of

100

of them would produce a confidence interval that contained the mean salary of all teachers from this state.

Choose the correct answer below.

A.

This conclusion is​ correct, assuming all assumptions and conditions are met.

B.

This conclusion is incorrect. All

100

of the intervals will contain the true mean​ salary, but different samples of

251

teachers will produce different confidence intervals.

C.

This conclusion is incorrect. About

99

out of

100

teachers surveyed will earn a salary within the interval.

D.

This conclusion is incorrect. About

99

out of

100

intervals will produce a confidence interval that overlaps with this interval.

​c) About

99

out of

100

teachers from this state earn between

​$43 comma 623

and

​$45 comma 465

.

Covid -19

1. state & explain the economic problem/s

2.why you have chosen your topic

3. What is the aggregate demand concerns regarding the topic/ who will be impacted

4. What are the positive & negative externalities, if any

5. What are your recommendations (effective/creative) provide at least 2 - 3

6. What are the alternatives ( effective/creative) provide at least 2 - 3

7. What are your solutions ( effective/ creative)

Paper length will be at minimum a 2 paged, word processed, hand - delivered paper.

1. Suppose that you ran the following regression:

Wage = Bo + B1Education +e

Where wage is in 1000's of dollars. Now Suppose that your econometrics give you the following results

N= 42

1. Estimate a 95% confidence interval for B1 Show your work carefully. What does this Confidence interval tell us about the relationship between education and wages?

2. Test at the 99% level the null hypothesis that B1 is zero, versus the alternative hypothesis that it's not Show your work and write the result clearly. Also write your conclusion. Interpret your result in words using economic theory.

3. Test at the 95% level the null hypothesis that Bo is zero, versus the alternative that it's positive. Show your work, the result and write your conclusion. Explain in words what does the conclusion mean.

4. Your manager thinks that 1 additional year of education will lead to an increase in wages by 1500 dollars. Choose an alternative hypothesis and explain your choice. Does your estimated relationship support this claim? Use a 5% significance level.

(15) The investment department of Big Bucks Businesses (BBB) is examining several different strategies. The forecasting department has indicated that each economic state is equally likely to occur. The estimated return for each security under each state is below. Tarragon Inc. manufactures decorative bottles, and Vintner Corp. is a mining firm. The following table summarizes the data: Economic State Tarragon Vintner Recession -11% 4% Average 20% 8% Boom 40% 6% a. Sara believes that BBB should invest 80% in Tarragon and 20% in Vintner. What is the return and variance on this portfolio? Use the population variance for the securities. b. Can Sara find a combination of Tarragon and Vintner that has no risk? If so, how much should BBB invest in each one? If not, explain why not. Hint: Check the correlation.

Suppose that the production function is given by Y=K^(1/2)L^(1/2)

a. Derive the steady state levels of capital per worker and output per worker in terms of the saving rate, s, and the depreciation rate, δ.

b. Suppose δ = 0.05 and s = 0.2. Find out the steady state output per worker.

c. Suppose δ = 0.05 but s increases to 0.5. Find out the steady state output per worker and compare your result with your answer in part b. Explain the intuition behind your results.

Activity 5a Gravity and Mass of the Earth Objectives: The purpose of this lab is to measure g, the acceleration of gravity at the surface of earth, and use it to calculate the mass of the Earth. Introduction: The Gravitational Constant The force felt on an object on earth is due to gravity which is defined with the relations: F_g = mg (1) Where Fg is the force due to gravity and m is the mass of the object and g is the acceleration due to gravity that is felt on the Earth's surface. The value of g depends on the mass of the Earth and the distance from the center of the Earth, as well as the universal gravitational constant, G. Thus the force felt on an object due to gravity can also be defined as: F_g=GMm/R^2 (2) Where M is the mass of the Earth, m is the mass of the object, and R is the distance to the center of the Earth to the center of the object. Activity I: Mathematical activity Put the two equations together and write g in terms of G, M, and R. Does the acceleration due to gravity, g, depend on the mass of the object being accelerated? Acceleration of a Dropped Object When an object is dropped from a height h above the surface of the earth, the amount fallen by the object is time dependent and it is given by the relation: h=1/2 gt^2 (3) The new term t in equation (3) is the time it takes for the object to drop. Equipment: A golf ball (or similarly heavy, small object); A stopwatch (can be a phone); Height of at least 4-5 meters (about 15ft); A string and ruler, or other method of measuring height Activity II: Dropping Objects With equation (3) g can be deduced if h and t are known. Thus we will measure both the height and time it takes to drop in other to deduce g. First, select a place to drop your ball, and measure the height. One method is to use a piece of string long enough to reach from the top to the bottom, and then measure the length of the string. This may be easiest with the help of a friend to hold the other end of the string or tape measurer. Make sure to use a metric measuring device (meters). If you only have a way to measure feet you will have to convert to meters (1ft = .305m) What is the height you will drop from? (in meters) We also need to characterize our measurement error/uncertainty. You should think about whether or not you stretched your string at any point, how big your ruler was compared to the string, and how finely you could measure the string compared to the ruler. With this in mind, estimate how far off your measured height could be from the actual height in meters. This is called the uncertainty in height. You can calculate the percent uncertainty by dividing the uncertainty in height by the total height measurement. What is your percent uncertainty for the height measurement? Time the Drop. Do not record the first two drops as you get used to the setup. Repeat 20 more times in order to make sure you've timed the drop of the ball well. This minimizes some of the errors that have to do with stopping and starting the stopwatch at the right time. Be careful to drop the ball from the exact height you measured, and to drop the ball rather than throw it. Tabulate your results below Drop # Time/(s) Drop # Time/(s) Drop # Time/(s) 1 8 15 2 9 16 3 10 17 4 11 18 5 12 19 6 13 20 7 14 Find the average time of all the 20 drop times in the table above. Estimate the error ∆t in the time measurements using the relations. ∆t=(t_high-t_low)/2 (4) Rearrange equation (3) and write g in terms of h and t. Use your measured values for h and t to calculate g. It is essential to note that g has been reported precisely at g = 9.8m/s2. Calculate the difference (subtraction) between the reported value of g and the value you calculated in the previous step. The difference between the two numbers (the reported constant and your calculated value) is due to errors in the measurement of h and t. In your estimation, which error had a larger effect on the result, Δh or Δt (hint: compare their percent uncertainties)? Next, we are going to use the errors in the measurement of h and t to calculate the range of possible values of g. Let’s define: t_max=t+∆t t_min=t-∆t h_max=h+∆h h_min=h-∆h Such that the upper value of g will be calculated with h_max and t_min and lower values of g will be calculated with h_min and t_max with the relations; g_max=(2h_max)/(t_min^2 ) and g_min=(2h_min)/(t_max^2 ) What are your upper and lower values for g? Is the real value of g between your calculated g_min and g_max? What does it mean if the real value of g is not within your range of possible g? Part III: Mass of the Earth For this section we will use equations (1) and (2). In order to find the mass of the earth, the universal constant G and the radius of the earth R are needed. The known values are: G=6.67×10^(-11) m^3⁄(kgs^2 ) R=6.40×10^6 m The reason we are giving you the value for R and using it to calculate M (instead of the other way around) is because R is much easier to measure than M. The radius of the Earth can be measured with a few observations and some geometry. The mass is much harder to measure directly. In the earlier section we wrote g in terms of M, R, and G. In this section you should put equation (1) and (2) together and find M in terms of g, G and R What equation did you come up with? Calculate a value for M using the g value you obtained earlier (in the part above). Use your g_min and g_max to calculate a Mmin and Mmax. Calculate the real value of M using the real value of g = 9.8m/s^2. How does it compare to your value of M (calculate the difference)? Is the real value of M between your Mmin and Mmax? Do you think this experiment is a reliable way to calculate the mass of the Earth? Explain. Part IV: Sources of Error List 3 things that made your measurement of g more uncertain. Of the three sources of error you have listed, pick one and explain what changes you could make to reduce or eliminate this error/uncertainty.

This exercise assumes familiarity with counting arguments and probability.

Kent's Tents has four red tents and three green tents in stock. Karin selects four of them at random. Let X be the number of red tents she selects. Give the probability distribution. (Enter your probabilities as fractions.)

Find

P(X ≥ 2).

(Enter your probability as a fraction.)

P(X ≥ 2) =