An automobile manufacturer claims that its cars average more than 410 miles per tankful (mpt).
As evidence, they cite an experiment in which 17 cars were driven for one tankful each and
averaged 420 mpt. Assume σ = 14 is known.

a. Is the claim valid? Test at the 5 percent level of significance.

b. How high could they have claimed the mpt to be? That is, based on this experiment, what is the maximum value for µ which would have been rejected as an hypothesized value?

c. What is the power of the test in part (a) when the true value of µ is 420 mpt? (Hint: Your rejection region for part (a) was stated in terms of comparing Zobs with a cut-off point on the Z distribution. Find the corresponding x̅cut-off and restate your rejection region in
terms of comparing the observed x̅value with the x̅cut-off. Then assume H1 is true (i.e. µ
= 420 mpt) and find the probability that x̅is in the rejection region.)

An automobile manufacturer claims that its van has a 38.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 240 vans, they found a mean MPG of 38.1. Assume the standard deviation is known to be 2.0. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Enter the value of the test statistic.

You are driving along straight road. You cover 200 miles in 4 hours? Does that mean that your speedometer read 50 mph for your entire trip? Is is necessary that your speedometer register 50 mph at least once during the trip? Use math to explain your answer.

I understand that your speedometer would not be 50mph for the entire trip, but I am not sure how to explain it using math.

Compute and Interpret Liquidity, Solvency and Coverage Ratios
Selected balance sheet and income statement information for Calpine Corporation for 2004 and 2006 follows.

(a) Compute the following liquidity, solvency and coverage ratios for both years. (Round your answers to two decimal places.)
2006 current ratio = Answer
2004 current ratio = Answer

2006 quick ratio = Answer
2004 quick ratio = Answer

2006 liabilities-to-equity = Answer
2004 liabilities-to-equity = Answer

2006 total debt-to-equity = Answer
2004 total debt-to-equity = Answer

2006 times interest earned = Answer
2004 times interest earned = Answer

2006 cash from operations to total debt = Answer
2004 cash from operations to total debt = Answer

2006 free operating cash flow to total debt = Answer
2004 free operating cash flow to total debt = Answer

(b) Which of the following best describes the company's credit risk?

Both the quick ratio and current ratio for 2006 are lower than 1.0 and have increased in the past two years. Along with interest coverage ratios that are exceedingly high, the probability that the company will face default has significantly increased.

Both the quick ratio and current ratio for 2006 are lower than 1.0 and have decreased in the past two years. Along with interest coverage ratios that are exceedingly low, the probability that the company will face default has significantly increased.

Both the quick ratio and current ratio for 2006 are above 1.0 and have decreased in the past two years. Along with interest coverage ratios that are exceedingly low, the probability that the company will face default has significantly decreased.

Both the quick ratio and current ratio for 2006 are above 1.0 and have increased in the past two years. Along with interest coverage ratios that are exceedingly high, the probability that the company will face default has significantly decreased.

Q: During a televised, title prize fight at a Las Vegas hotel, Luis threw a punch which hit Michael in the face. As a result:

a: This would ordinarily be an act of negligence, however since Michael consented to the fight, he has no viable legal action against Luis. INCORRECT

b: This would ordinarily constitute strict liability for engaging in an inherently dangerous activity, however since Michael consented to the fight, he has no viable legal action against Luis.

c: This would ordinarily be an action of intentional infliction of emotional distress, however since Michael consented to the fight, he has no viable legal action against Luis.

d: This would ordinarily be a battery, however since Michael consented to the fight, he has no viable legal action against Luis.

Problem 8-21 (Algorithmic)

Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:

Type I rooms do not have wireless Internet access and are not available for the Business rental class.

Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 140 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 125 Type I rooms and 135 Type II rooms.

1. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types.
   

   Variable	# of reservations
   SuperSaver rentals allocated to room type I
   SuperSaver rentals allocated to room type II
   Deluxe rentals allocated to room type I
   Deluxe rentals allocated to room type II
   Business rentals allocated to room type II

2. How many reservations can be accommodated in each rental class?
   

   Rental Class	# of reservations
   SuperSaver
   Deluxe
   Business

Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. The Classic Corvette Owners Association scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are possible: convention customers/two-night package; convention customers/Friday night only; convention customers/Saturday night only; regular customers/two-night package; regular customers/Friday night only; and regular customers/Saturday night only.

The cost for each type of reservation is shown here:

The anticipated demand for each type of reservation is as follows:

Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue.

1. Define the decision variables and state the objective function. Round your answers to the nearest whole number.
   

   Let	CT = number of convention two-night rooms
   	CF = number of convention Friday only rooms
   	CS = number of convention Saturday only rooms
   	RT = number of regular two-night rooms
   	RF = number of regular Friday only rooms
   	RS = number of regular Saturday only room

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

2. Formulate a linear programming model for this revenue management application. Round your answers to the nearest whole number. If the constant is "1" it must be entered in the box.
   

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

   S.T.

   1)	CT
   2)	CF
   3)	CS
   4)	RT
   5)	RF
   6)	RS
   7)	CT	+	CF
   8)	CT	+	CS
   9)	CT	+	CF	+	RT	+	RF
   10)	CT	+	CS	+	RT	+	RS
   11)	CT,	CF,	CS,	RT,	RF,	RS			0

3. What are the optimal allocation and the anticipated total revenue? Round your answers to the nearest whole number.
   

   Variable	Value
   CT
   CF
   CS
   RT
   RF
   RS

   
   Total Revenue = $  
   
4. Suppose that one week before the convention the number of regular customers/Saturday night only rooms that were made available sell out. If another nonconvention customer calls and requests a Saturday night only room, what is the value of accepting this additional reservation? Round your answer to the nearest dollar.
   
   The dual value for constraint 10 shows an added profit of $   if this additional reservation is accepted.

A hotel has 100 rooms. On any given night, it takes up to 105 reservations, because of the possibility of no-shows. Past records indicate that the number of daily reservations is uniformly distributed over the range 96-105. That is, each integer number in this range has a probability of 10%, of showing up. The no-shows are represented by the distribution in the table below.

Based on your thirty simulations, determine the following measures of performance of this booking system: the expected number of rooms used per night and the percentage of nights when more than 100 rooms are claimed. (Show your simulations and any other information used in the analysis. Don’t send any worksheet.)

Scenario: Chief Complaint: Fever , AIDS. 40 year old white male resides at the hotel and lives on social security disability; diagnosed with AIDS, end stage, addiction, and agoraphobia presents with fever X2 weeks, no thermometer available, diarrhea daily. He tends to miss appointments because of his extreme anxiety in public places. He has not been on antiretroviral therapy due to his inability to regularly take medications. He is not in contact with case management, but there is a special hospice for homeless people with AIDS and perhaps it might be time to consider a referral for more supportive services.

Vital signs: 100/70 64 18 99.8 BMI:17   Gen: thin white male

skin: dry and flacking multiple nevi ruddy complexion, red flaky, rash on naso/ labial folds, and scalp + DANDROFF

HEENT:  Poor definition, gengevitus, shotty lymph nodes posterior / Anterior cervical.

Question: How would APRN (Nurse practitioner) prepare for home visit? Explore the practical concerns, the equipment APRN need to bring, and goals for the patient’s care.

Question: What might you want as Nurse practitioner to know from the case management and supportive services team?

Question: What specific things would you assess as Nurse practitioner at this visit?

Question: What are the essential elements of the history and physical today?

Question: What is your assessment as Nurse Practitioner ?

Question: What is your plan?