A production line operation is tested for filling weight accuracy using the following hypotheses.

Hypothesis       Conclusion and Action
H ₀:  = 16         Filling okay, keep running
H _a:     16       Filling off standard; stop and adjust machine

The sample size is 36 and the population standard deviation is  = 0.8. Use  = .05. Do not round intermediate calculations.

1. What would a Type II error mean in this situation?
   Concluding that the mean filling weight is not 16 ounces when it actually isConcluding that the mean filling weight is 16 ounces when it actually isn'tItem 1
   
2. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?
   
   
3. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?
   

Based on current dividend yields and expected capital gains, the expected return on portfolios A and B are 11% and 14% respectively. The beta of A is 0.8 while that of B is 1.5. The rate of exchange fund bill is currently 6%, while the expected return of the Hang Seng Index is 12%. The standard deviation of portfolio A is 10%, while that of B is 31%, and that of the index is 20%.

a. If you currently hold the Hang Seng Index, would you choose to add portfolio A or B to your holdings?

b. If you currently hold the exchange fund bills, which one would you choose (i.e. portfolio A, portfolio B or the Hang Seng Index) to add to your holdings?

c. What would happen if we measure the performance of a poorly diversified portfolio using Treynor measure? (6marks)

Pennsylvania Company has a monthly gross payroll (paid on the last day of each month) of $516,000, which is subject to unemployment taxes (Federal at 0.8% and State at 5.4%). All earnings are subject to 7.65% FICA tax (combined Social Security and Medicare). Federal income tax withholdings are 25%, and state income tax withholdings are 8% of total earnings.

Assuming no individual employee has reached the maximum limit for Social Security tax or for unemployment tax, which of the following is not true for the month ended January 31?

a) Pennsylvania Company will record a liability for Federal Unemployment Taxes of $4,128.

b) Pennsylvania Company will record a net payroll of $306,246.

c) Pennsylvania Company will record a liability for State Income Taxes of $41,280.

d) Pennsylvania Company will record a total liability for FICA Taxes of $39,474.

Please answer the following 2 questions using the probabilities of different scenarios below.

• What is the expected return and standard deviation of the S&P 500 portfolio and the Bond?

• Suppose AAPL has a beta of 0.8. If the risk-free rate is 3% and the market return is 9%, according to CAPM, the expected return for AAPL is? If the stock price for AAPL is $100 today, according to the expected return you calculate, what is the expected price for AAPL in a year if AAPL is not paying a dividend? What is the expected price if AAPL will pay a dividend of $3?

Suppose that the mean weight of newborn babies is normally distributed with a mean of 6.9 pounds and a standard deviation of 0.8 pound. A developmental psychologist wants to test whether newborn babies of mothers who use drugs during pregnancy differ in weight from the average baby. The psychologist takes a random sample of 30 mothers who used drugs during pregnancy and computes the mean birth weight of these mothers’ babies. This sample of 30 mothers has a sample mean of 6.7 pounds. Using an alpha level of .01, test whether mothers’ drug use during pregnancy affects newborn babies’ birth weight. Which of the following is the most accurate mathematical null hypothesis?

A) μ < 6.7

B) μ ≠ 6.7

C) μ ≠ 0

D) μ = 6.9

A healthy 26-year-old woman sustained a significant crush injury to her right upper extremity while on the job at a local construction site. She was brought to the emergency department and subsequently underwent pinning and reconstructive surgery and received perioperative broad-spectrum antibiotics. Her blood pressure remained normal throughout her hospital course. On the second hospital day, a medical consultant noted a marked increase in her creatinine, from 0.8 to 1.9 mg/dL. Her urine output dropped to 20 mL/h. Serum creatine kinase was ordered and reported as 3400 units/L.

Questions

What are the primary causes of this patient’s acute kidney injury? How should her kidney injury be categorized (as prerenal, intrarenal, or postrenal)?

How should she be treated?

A bakery must decide how many pies to prepare for the upcoming weekend. The bakery has the option to make 50, 100, or 150 pies. Assume that demand for the pies can be 50, 100, or 150. Each pie costs $5 to make and sells for $7. Unsold pies are donated to a nearby charity center. Assume that there is no opportunity cost for lost sales.

7) Refer to the information above.

a. Which alternative should be chosen based on the maximax criterion?

b. Which alternative should be chosen based on the maximin criterion?

c. Which alternative should be chosen based on the Lapalce criterion?

d. Which alternative should be chosen based on criterion of realism with alpha = 0.8?

e. Which alternative should be chosen based on the minimax regret criterion?

(PLEASE ANSWER IN EXCEL SPREADSHEET)

A mystery planet and its moon are found revolving around a nearby star. The star is a K3 Main Sequence star with a mass of approximately 0.8 M☉ and a radius of 0.78 R☉. The planet is believed to be terrestrial (Earth-like, and therefore of a similar density) and has an observed orbital period of 243 days. The moon orbits the planet every 13.2 hours with an average orbital radius of 19,600 km. Using this information, find:

(a)the orbital radius of the planet,

(b)the distance at which another planet in the system would have an orbital speed of 24,000 m/s,

(c)the point between the star and the planets at which the net force on a spacecraft would be zero, and

(d)the period of a 80-cm long simple pendulum with a mass of 30 grams that is swinging on the planet’s surface

Knarfappaz Co. pays no taxes and is financed entirely by common stock. The stock has a beta of 0.8 and a price-earnings ratio of 12.5 and is priced to offer an 8% expected return. Knarfappaz now decides to repurchase half the common stock and substitute an equal value of debt. If the debt yields a riskfree 5%, calculate: A. The beta of the common stock after the refinancing; B. The required return and risk premium on the stock before the refinancing; C. The required return and risk premium on the stock after the refinancing; D. The required return on the debt; E. The required return on the company (i.e., stock and debt combined) after the refinancing. Assume that the operating profit of the firm is expected to remain constant in perpetuity. Give: F. The percentage increase in expected earnings per share; G. The new price/earnings ratio (P/E).