Download the dataset returns.xlsx. This dataset records 83 consecutive monthly returns on the stock of Philip Morris (MO) and on Standard & Poor’s 500 stock index, measured in percent. Investors might be interested to know if the return on MO stock is influenced by the movement of the S&P 500 index. Please be aware that return is defined as new price − old price old price × 100%, so it is always reported as a percentage.

1. What is the response and explanatory variable for this dataset?

2. Create a scatterplot between the two variables and describe the form, direction, and strength of the linear relationship between the two variables.

3. Create a residual plot (residuals on y-axis, explanatory variable on x-axis).

4. Based on your answers to parts 2 and 3, are the assumptions for the regression model met? Address the linearity and constant variance assumptions.

5. Verify the values of the following: the sample means of the monthly returns of MO stocks and S&P stocks are 1.8783 and 1.3036 respectively; the sample standard deviations of the monthly returns of MO stocks and S&P stocks are 7.5539 and 3.3915 respectively.

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages. 1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4 (a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = % s = % (b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.) lower limit % upper limit % (c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.) lower limit % upper limit % (d) The home run percentages for three professional players are below. Player A, 2.5 Player B, 2.0 Player C, 3.8 Examine your confidence intervals and describe how the home run percentages for these players compare to the population average. We can say Player A falls close to the average, Player B is above average, and Player C is below average. We can say Player A falls close to the average, Player B is below average, and Player C is above average. We can say Player A and Player B fall close to the average, while Player C is above average. We can say Player A and Player B fall close to the average, while Player C is below average. (e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem. Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal. Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal. No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal. No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

(d) The home run percentages for three professional players are below.

Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.

A.) We can say Player A falls close to the average, Player B is above average, and Player C is below average.

B.) We can say Player A falls close to the average, Player B is below average, and Player C is above average.    

C.) We can say Player A and Player B fall close to the average, while Player C is above average.

D.) We can say Player A and Player B fall close to the average, while Player C is below average.

(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

A.) Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

B.) Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.    

C.) No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

D.) No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

(d) The home run percentages for three professional players are below.

Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.

We can say Player A falls close to the average, Player B is above average, and Player C is below average.

We can say Player A falls close to the average, Player B is below average, and Player C is above average.    

We can say Player A and Player B fall close to the average, while Player C is above average.

We can say Player A and Player B fall close to the average, while Player C is below average.

(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.    

No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

A contract is a set of legally enforceable promises. A valid contract must have agreement/ offer consideration, legal object/purpose, and parties with legal capacity.

Sometimes two parties will enter into a contract with the intent to benefit a third party. In these situations, a third-party beneficiary contract is formed. Third-party contracts are difficult to follow with the rights and obligations of the parties.

You are required to create a contract (keep it simple-one page). You will select the subject of the contract.

What would the contract look like? How would you design it? What would you want to be included? What legally be included?

Below is a simple example of the format of a contract. Do not copy the contract! Instead create your own, but make sure to include the most important elements shown below.

CONTRACT FOR THE SALE OF GOODS

Paragraph 1. _______________________, hereinafter referred to as Seller, and _____________________, hereinafter referred to as Buyer, hereby agree on this ____ day of _______________, in the year ____________, to the following terms.

Identities of the Parties

Paragraph 2. Seller, whose business address is _____________________, in the city of _______________, state of _________________________, is in the business of ___________________________. Buyer, whose business address is ____________________, in the city of _________________, state of _________________________, is in the business of ____________________________.

Description of the Goods

Paragraph 3. Seller agrees to transfer and deliver to Buyer, on or before ________________________ [date], the below-described goods:

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

Buyer's Rights and Obligations

Paragraph 4. Buyer agrees to accept the goods and pay for them according to the terms further set out below.

Paragraph 5. Buyer agrees to pay for the goods:

• In full upon receipt
• In installments, as billed by Seller, and subject to the separate installment sale contract of __________________ [date] between Seller and Buyer.
• Half upon receipt, with the remainder due within 30 days of delivery.

Paragraph 6. Goods are deemed received by Buyer upon delivery to Buyer's address as set forth above.

Paragraph 7. Buyer has the right to examine the goods upon receipt and has ____ days in which to notify seller of any claim for damages based on the condition, grade, quality or quality of the goods. Such notice must specify in detail the particulars of the claim. Failure to provide such notice within the requisite time period constitutes irrevocable acceptance of the goods.

Seller's Obligations

Paragraph 8. Until received by Buyer, all risk of loss to the above-described goods is borne by Seller.

Paragraph 9. Seller warrants that the goods are free from any and all security interests, liens, and encumbrances.

Attestation

Paragraph 10. Agreed to this _____ day of _____, in the year ____________.

By: ___________________________ Official Title: ____________________________

On behalf of ______________________________________, Seller

I certify that I am authorized to act and sign on behalf of Seller and that Seller is bound by my actions. ______ [initial]

By: ___________________________ Official Title: ____________________________

On behalf of _____________________________________, Buyer

I certify that I am authorized to act and sign on behalf of Buyer and that Buyer is bound by my actions. ______ [initial]

[NOTARY STAMP HERE]

JB Co. is planning to invest in a new koala theme park. The investment will generate $4.5 million p.a. for 15 years with the first cash inflow received in one year's time. The required rate of return for this type of investment is expected to be 6% p.a. for years 1-9 rising to 11% p.a. for years 10-15. What is the most JB Co. should pay for this investment now?

What are some characteristics of a normal distribution? What does the empirical rule tell you about data spread around the mean? How can this information be used in quality control?

Can you compare apples and oranges, or maybe elephants and butterflies? In most cases the answer is no – unless you first standardize your measurements. What are a standard normal distribution and a standard z score?

A magazine reported the results of a random telephone poll commissioned by a television network. Of the 1144 men who​ responded, only 32 said that their most important measure of success was their work. Complete parts a through c. a right parenthesis Estimate the percentage of all males who measure success primarily from their work. Use a 95​% confidence interval.​ Don't forget to check the conditions first.

Question 1)

Why do successive steps in the alpha addition process, which forms the nuclei C12 through 56 Fe, require greater and greater temperature and pressure?

Question 2)

Why are nucleosynthetic processes in first generation starts limited to H fusion during most of the life of the star?

Question 3

How do we know the sun is at least a "second generation" star?

A consonsultant wishes to invest up to a total of $25000 in two types of securities, one that yields 10% per year and another than yields 8% per year. They believe that the amount invested in the first security should be at most one third of the amount invested in the second security. What investment program should the consultant pursue in order to maximize income? (Use constraint inqualities with objective function)