1. The concept of mutual assent is also called a/an: ___ Agreement of sorts. ___ Meeting of the minds. ___ Intent to negotiate. ___ Void contract. ___ Contract in rem.

2. If the offeror revokes her offer before acceptance by the offeror, the offer is: ___ Terminated, by operation of law. ___ Terminated, by action of the parties. ___ Not terminated, because all offers are irrevocable. ___ None of the above.

3. The mailbox rule determines the effective date of the: ___ Acceptance ___ Revocation ___ Rejection ___ Postmark ___ Mutual assent

4. The night before his commencement ceremony, Leland’s uncle promises to buy him a new car after he actually sees Leland receive his diploma. Leland gladly accepts. After the ceremony, Leland’s uncle says, “Just kidding, no car!” Leland cannot prevail in a breach of contract claim because the agreement lacks: ___ Offer ___ Acceptance ___ Consideration ___ Legality ___ Mutual assent

5. Which of the following does not result in the termination of an offer? ___ Revocation ___ Acceptance ___ Rejection ___ Death of the offeror ___ Destruction of the subject matter

Nonparametric Methods
In this assignment, we will use the following nonparametric methods:

• The Wilcoxon signed-rank test: The Wilcoxon signed-rank test is the nonparametric test analog of the paired t-test.
• The Wilcoxon rank-sum test or the Mann-Whitney U test: The Wilcoxon rank-sum test is an analog to the two-sample t-test for independent samples.

Part 1: Wilcoxon Signed-Rank Test

Let's take a hypothetical situation. The World Health Organization (WHO) wants to investigate whether building irrigation systems in an African region helped reduce the number of new cases of malaria and increased the public health level.

Data was collected for the following variables from ten different cities of Africa:

• The number of new cases of malaria before the irrigation systems were built
• The number of new cases of malaria after the irrigation systems were built

Table 1: Cases of Malaria

Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:

• Run a sample Wilcoxon signed-rank test to show whether there is a statistically significant difference between the number of cases before and after the irrigation systems were built.
• Obtain the rank-sum.
• Determine the significance of the difference between the groups.
• Determine whether building these systems helped reduce new cases of malaria.
• In a Microsoft Word document, provide a written interpretation of your results.

Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. The data are recorded in the table below. Do you think that their cholesterol levels were significantly lowered? Conduct a hypothesis test at the 5% level.

1. In words, state what your random variable X_d  represents.

a. X_d represents the total difference in cholesterol levels before and after the diet.

b. X_d represents the difference in the average cholesterol level before and after the diet.    

c. X_d represents the average difference in the cholesterol level before and after the diet.

d. X_d represents the average cholesterol level of the 10 individuals.

2.State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

3.What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

4.What is the p-value?

5.Explain how you determined which distribution to use.

a. The standard normal distribution will be used because the samples are independent and the population standard deviation is known.

b. The t-distribution will be used because the samples are dependent.    

c. The t-distribution will be used because the samples are independent and the population standard deviation is not known.

d. The standard normal distribution will be used because the samples involve the difference in proportions.

When subjects were treated with a drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the table below. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Using a 0.05 significance level, is there sufficient evidence to support the claim that the drug is effective in lowering systolic blood pressure?

Before   After
179   147
167   177
158   159
172   148
188   179
196   145
210   179
175   162
157   152
205   143
169   157
164   148

n this example,?

?d?

is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the systolic blood pressure reading before the drug was taken minus the reading after the drug was taken. What are the null and alternative hypotheses for the hypothesis test?

A. H0: ?d=0       H1: ?d>0

B. H0: ?d?0       H1:?d=0

C. H0: ?d?0      H1:?d>0

D. H0: ?d=0      H1:?d<0

Identify the test statistic.

t= _______

(Round to two decimal places as needed.)

Identify the P-value.

P-value= _______

(Round to three decimal places as needed.)

Since the P-value is      Less///or////Greater_____??than the significance level, Fail to Reject////or///Reject Ho.

There is?Insufficient//or//sufficient____?evidence to support the claim that the drug is effective in lowering systolic blood pressure.

?

H0.?

There is evidence to support the claim that the drug is effective in lowering systolic blood pressure.

A new type of bird capable of self-propulsion is designed in order to maximise its flying distance in the presence of aerodynamic drag. This new bird, having the initial mass of mo, generates thrust by ejecting 1% of its initial mass (0.01mo) with the velocity of 50m/s in the direction opposite to the bird’s instantaneous velocity relative to the bird every 0.1s (similar to how rockets generate thrust).

function [vx_f,vy_f,m_f] = mass_ejection(vx_i,vy_i,v_eb,m_i,m_e)

% Inputs:

% vx_i: Velocity component in x direction before ejection

% vy_i: Velocity component in y direction before ejection

% v_eb: Ejection velocity of the mass relative to the bird

% m_i : Mass of the bird before ejection

% m_e : Ejection mass

% Outputs: % vx_f: Velocity component in x direction after ejection

% vy_f: Velocity component in y direction after ejection

% m_f : Mass of the bird after ejection

(d) Using the function written incorporate the mass ejection mechanism into the existing model with drag (remember that you need to run this function every 0.1s and use the output to update the velocity and mass of the bird). Compute and plot the trajectory of the new bird and compare it with the trajectory of the original bird with the same initial conditions. On your plot, indicate with symbols where mass ejections happen. The bird is launched with the initial velocity of 10m/s at the angle of 50? from the horizontal. The initial mass of the bird, mo is 1kg. The release point of the bird is 2m directly above the base of slingshot and the base of slingshot can be considered as the origin (figure 5). The density of air is 1.2 kg/m3 and use CD = 1. The bird can be treated as a sphere with a radius of 0.15 m. on matlab

7. Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). The hypothetical data provided below from 10 trials report the mean pressure applied to the driver’s head during a crash test for each type of car.

Compact: 635, 671, 648, 685, 648, 651, 654, 682, 687, 627

Midsize: 482, 529, 541, 518, 497, 526, 507, 492, 499, 451

Full-size: 451, 483, 464, 447, 456, 499, 484, 492, 449, 449

10. An instructor teaching algebra 1 to ninth-grade students wishes to analyze the difference between student achievement before and after the implementation of an online help resource. For 6 weeks, students worked with conventional, in-class and homework resources, and then for the next 6 weeks, an online help desk was made available to them. The scores for 6 students on a district benchmark test before and after the implementation of the online help resource are listed below.

Before: 22, 18, 33, 20, 23, 27

After: 28, 21, 32, 25, 33, 28



12. A college counselor wonders whether second semester students take fewer units than first semester students. From the population of each group (first semester and second semester), she selects 10 students at random. The following data were collected:

First semester students: 10, 12, 14, 14, 15, 15, 15, 16, 16, 18

Second semester students: 6, 9, 9, 10, 12, 12, 13, 14

Your all-equity firm generates $60M per year in perpetual free cash flows. The firm pays out the entire free cash flows to stockholders each year and is about to pay the $60M generated this year. Analysis of comparable firms tells you that your asset cost of capital is 15 percent. Assume that there are 1M shares outstanding and the capital market is perfect.

a)What is the price per share for this firm att=0 just before the firm paysout the $60M?This price is called the cum-dividend price.

b)Suppose the firm chooses to pay out the $60M as a dividend.What is the price per shareat t=0 just after the dividend is paid out?This price is called the ex-dividend price.

c)The firm would like to pay$100M worth of dividends at t=0 and thus needs another $40M. The firm plans to issue shares today (t=0) at the cum-dividend price from (a) so that it will have the extra $40M.
i.How many additional shares does the firm have to issue to raise $40M?
ii.Whatwould the price per share be at t=0 just before this $100M dividend is paid out? (but directly after the additional $40M was raised via equity issuance)(Hint: The firm added $40M of cash to its assets throughthe equity issuance. That is,the firm’s asset value is $40M higher than before.)
  iii.What would the price per share be at t=0 just after the $100M dividend is paid out?

d)Which of the following is true? Explainyour answer.①.Investors prefer the usual dividend in (b).②.Investors prefer the boosted dividend in (c).③.Investors are indifferent between the usual and boosted dividends

1. Which leverage ratio yields the highest expected return on equity?
2. Which leverage ratio yields the highest variability (risk) in expected return on equity?
3. What assumptions was made about the cost of debt (that is, the interest rates) under the various capital structures (that is, the leverage ratio)? How realistic is the assumption?

QUESTION 1:

Researchers claim that women speak significantly more words per day than men. One estimate is that a woman uses about 20,000 words per day while a man uses about 7,000. To investigate such claims, one study used a special device to record the conversations of male and female university students over a four- day period. From these recordings, the daily word count of the 20 men in the study was determined. Here are their daily word counts:

What value we should remove from observation for applying t procedures?

A 90% confidence interval (±±10) for the mean number of words per day of men at this university is from  to  words.

Is there evidence at the 10% level that the mean number of words per day of men at this university differs from 9000?

QUESTION 2:

Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. Here are the sweetness losses ( sweetness before storage minus sweetness after storage) found by 10 tasters for one new cola recipe:

Take the data from these 10 carefully trained tasters as an SRS from a large population of all trained tasters.

Is there evidence at the 5% level that the cola lost sweetness? If the cola has not lost sweetness, the ratings after should be the same as before it was stored.

The test statisic is t =  (±±0.001)

This is c++ code.

Create a file sort.cpp. to mix functions with the selection sort algorithm:

·Write a function int least(vector<string> strs, int start)to return the index of the smallest value in the vector. You are to assume there is at least one value in the vector.

·Write a function void selsort(vector<string> & strs) to use selection sort to sort the vector of strings. It is a worthwhile experiment to try leaving out the & and seeing that the vector stays exactly the way it is, but remember to put it back in before submitting.

·You need to use the above function here

·Once you know the elements you want to swap, call the library swap(T& a, T& b) function to do the swap, which after the 2011 standard, has been moved from <algorithm> to the <utility> library (though I think IDE’s automatically include this, so you probably won’t need to explicitly #include it). The &’s in the prototype of the function allow it to actually move your values, but you should not be using &’s when calling the function

·Write main() to test your selection sort. You just need to output the

·Try at least two calls, one where the elements are already in order and one where you need at least two swaps to order the values. For the following run, the first call was done with “lion”, “tiger”, while the 2^nd call was done with “lion”, “tiger”, “zebra”, “bear” (the first swap is of “lion” and “bear”, so the 2^nd iteration starts with “bear”, “tiger”, “zebra”, “lion” and “lion” needs to be swapped to the second position)

Before: lion tiger

After: lion tiger

Before: lion tiger zebra bear

After: bear lion tiger zebra