5 Three Pirates Sharing 100 Gold Coins

Three pirates of different ages have a treasure of 100 gold coins. They decide to split the coins using this scheme:

• The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.

  • – If more than 50% (exclusive) of the pirates vote for it, then the coins will be shared that way and the game ends. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. Note that if exactly 50% of the pirates vote for it, then the pirate proposing the scheme will be thrown overboard.

  • – As pirates tend to be a bloodthirsty bunch. If a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

• Assuming that all 3 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates).

1. What will happen?

2. Assume now Captain Hook spots the scene and wants to share the gold as well. That is, now we have four pirates sharing the coins. Captain Hook will be the first to propose a scheme to share the coins. Assume the same rule applies. What will happen?

A researcher was interested in the effects of caffeine on sleep. She measured how many minutes it took for ten participants to fall asleep. Half of the participants drank a liter of caffeinated soda before going to sleep while the other half were only allowed to drink water. Summary data of minutes are presented below. Did the caffeine increase the length of time it took to fall asleep (a =.05)? (27 points total for 6a-e)

         Water Group Caffeine Group

                     18 22

                     15 15

                     19 20

                     14 21

                     14 19

a. Name the test to be conducted and why you selected it:

b. State the null and alternative hypotheses:

c. State the CV and the decision rule. Sketch the rejection region:

d. In SPSS, calculate the observed test statistic. Paste your answer here or attach it to your assignment. In addition, calculate the value of eta2 (h2).

e. Write out an APA style conclusion based on this finding:

1. For each of the following terms, write a sentence that properly uses one or more terms in context; underline the term(s) used in each sentence: Chemical reaction Products (of a chemical reaction) Dependent variable (of data collection) reactants (of a chemical reaction) aerobic cellular respiration independent variable (of data collection)

Provide 3 reasons why refluxing is a useful technique as opposed to heating a reaction solution in a temperature bath to perform a reaction

Two point charges are arranged so there is a small distance between them. One charge is positive and the other is negative. If the two charges have different magnitudes, there is a spot (not at infinity) where the total electric field is zero.

Using Grocery Rewards ~ A Gallup Poll of 500 randomly selected American adults resulted in 405 stating they use a grocery stores’ rewards card to save money on their grocery purchases. A local grocery store manager comes to you for help to use these results to provide an estimate of the population proportion of all American adults who use a grocery stores’ rewards card to save money on their grocery purchases. You ask the manager what confidence level should be used ~ 90%, 95%, 98% or 99%. The manager says “I am not sure what the confidence level really means, but use 98% I guess”.

You create the following list to help you remember the various items you need to include in your response back to the manager:

Assumptions: You know you may assume a random sample of 500 American adults was selected. You plan to both state and check the remaining necessary assumption.
Computations: You will compute and report the 98% confidence interval, showing all work so the manager can follow your computations.
Level Explanation: Since the manager was unclear what the confidence level means, you will include a sentence to explain it, that is, provide an interpretation of the 98% confidence level in context.

You are asked to prepare a pH=4.00 buffer starting from 1.50 L of 0.0200M solution of benzoic acid (C6H5COOH) and an excess of sodium benzoate (C6H5COONa).

Part A

What is the pH of the benzoic acid solution prior to adding sodium benzoate?

Express your answer using three significant figures.

Part B

How many grams of sodium benzoate should be added to prepare the buffer? Neglect the small volume change that occurs when the sodium benzoate is added.

Express your answer using two significant figures.

List the benefits of budgeting in a business. Also list and describe the components of a Master Budget.

When conducting a statistical hypothesis test, a very small p value indicates strong evidence against the null hypothesis. Why?

The largest use of nitric acid is in the reaction with ammonia to produce ammonium nitrate for fertilizer.

A) If 275.0 g of nitric acid reacted with 156.5 g of ammonia, what is the limiting reagent?

B) How many grams of ammonium nitrate would be produced?

C) If only 300 g of ammonium nitrate was produced, what is the percent yield?

1. What is Financial Statement Analysis (FSA)?
2. How is FSA related to AND different from financial accounting and auditing?
3. What is a typical day in the life of a financial analyst?
4. How do you become a financial analyst? What professional licenses or education do you need or can you get?

Python

Without running / testing the following code, predict what the following program prints on the screen.

freeze = int(32)

boil = int(212)

freeze = 0

boil = 100

print(freeze, boil)

• Write a program that asks the user for a number in the range of 1 through 7. The program should display the corresponding day of the week, where 1 = Monday, 2 = Tuesday and so forth. If the user types in a 6 then "Saturday" should be printed on the screen.
• The program should display an error message if the user enters a number that is outside the range of 1 through 7.
• Name the source code file
• Test and run the program. Capture the output console and save it as an image file

The medium-run equilibrium is characterized by four conditions:

- Output is equal to potential output (Y=Y_n)

- The unemployment rate is equal to the natural unemployment rate (u=u_n)

- The real policy interest rate is equal to the "natural" rate of interest (the one that makes aggregate demand equal to potential output).

- The expected rate of inflation is equal to the actual rate of inflation.

(a) Assume that the level of expected inflation is formed in such a way that this year's expected inflation is equal to last year's inflation: πe=πt−1πe=πt−1. What is the behavior of the rate of inflation in a medium-run equilibrium?

Select one:

a. it will not change, meaning that the price level remains constant year after year.

b. it will be constant and equal to an exogenous constant, that does not depend on past inflation.

c. it will be increasing or decreasing depending on the value of the natural interest rate.

d. it will not change: the value of inflation is simply equal to its value in the previous period.

(b) Now assume, instead, that the level of expected inflation is equal to an exogenous constant:

πe=π¯πe=π¯

What is the behavior of actual inflation in the medium-run equilibrium?

Select one:

a. it is increasing or decreasing, depending on the value of the "natural" rate of interest

b. It is constant, and equal to its previous period.

c. It is stable and equal to the exogenous constant π¯π¯

d. inflation is increasing at a rate equal to π¯

(c) Imagine that the economy is in a medium-run equilibrium. Assume that expected inflation is equal to past inflation (πe=πt−1πe=πt−1).

In this situation, the Government decides to increase public spending (G), while leaving taxes unchanged. How will macroeconomic variables react to this fiscal expansion?

Select one:

a. output will increase; the unemployment rate and nominal wages will remain the same (equal to the values determined by the WS-PS model); the inflation rate will start increasing year after year.

b. output will decrease; the unemployment rate and nominal wages will remain the same (equal to the values determined by the WS-PS model); the inflation rate will start decreasing year after year.

c. output will increase; the unemployment rate will decrease; nominal wages will remain the same; the inflation rate will start increasing year after year.

d. output will increase; the unemployment rate will decrease; the growth rate of nominal wages and the inflation rate will start increasing year after year.

(d) How must the Central Bank react to the increase in G, in order to ensure that the economy sticks to the medium-run equilibrium?

Select one:

a. it must increase the interest rate.

b. it must decrease the interest rate.

c. it must ensure that the interest rate remains unchanged.

d. it must do nothing: output is already equal to potential output.

e. it must increase taxes.

A union leader in the Maritime Workers' Union believed that workers at the Port of Brisbane were receiving a lower weekly salary than workers at Port Kembla. To determine whether this claim was valid, they took samples of size 17 and 11 in Brisbane and Port Kembla, respectively, and found that the average and standard deviation of the weekly salaries were $914.11 and $49.38 respectively in Port Kembla, and $859.23 and $55.62 in Brisbane. Use Brisbane minus Port Kembla, and answer correct to two decimal places. 1. Determine a point estimate for the difference in the average weekly salary between the two ports. ? 2. Calculate the standard error for the difference between sample means assuming that the workers' salaries in both locations are normally distributed and have the same population variance. ? 3. Use Kaddstat to determine a 95% confidence interval for the difference between the mean weekly salaries in Brisbane and Port Kembla. lower limit ? upper limit ?