The next three questions are based on the following information.

To study the weight accuracy of a 50lb fertilizer bag, 12 samples of 12 bags of fertilizer in each sample were taken and the results are as follows.

1.

The overall average weight of a bag of fertilizer is ________ pound, and the average range is ____________ pound. (Please round to two decimal points and include no units.)

2.

The upper control limit for a 99.7% control chart for the mean is ________ pound, and the lower control limit is __________ pound. (Please round to two decimal points and include no units. Please enter the upper limit first.)

3.  

The upper control limit for a 99.7% control chart for the range is_________ pound, and the lower control limit is _________ pound. (Please round to two decimal points and include no units. Please enter the upper limit first.)

Cardio Care Inc. manufactures stationary bicycles and treadmills. The products are produced in the Fabrication and Assembly production departments. In addition to production activities, several other activities are required to produce the two products. These activities and their associated activity rates are as follows:

The activity-base usage quantities and units produced for each product were as follows:

Use the activity rate and usage information to compute the total activity costs and the activity costs per unit for each product. If required, round your answers to two decimal places.

Data: S₀ = 105; X = 112; 1 + r = 1.1. The two possibilities for S_T are 134 and 90.

a. The range of S is 44 while that of P is 22 across the two states. What is the hedge ratio of the put? (Round your answer to 2 decimal places. Negative value should be indicated by a minus sign.)

b. Form a portfolio of one share of stock and two puts. What is the (nonrandom) payoff to this portfolio?

c. What is the present value of the portfolio? (Round your answer to 2 decimal places.)

d. Given that the stock currently is selling at 105, calculate the put value. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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: Rental Class Super Saver Deluxe Business Type I $30 $35 -- Room Type II $20 $30 $40 Type I rooms do not have 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 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.

Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints.

A researcher examined whether the time of day someone exercises affects memory retention in college courses.  Participants were assigned to one of three exercise groups: morning, afternoon, evening, and their performance on a memorization task was measured.  This data is below:

Assuming the researcher wants to know whether the performance was different in these groups (alpha = .05).  What is the Mean Squares Within (SS_W)?  Round to two decimal places.

A researcher examined whether the time of day someone exercises affects memory retention in college courses.  Participants were assigned to one of three exercise groups: morning, afternoon, evening, and their performance on a memorization task was measured.  This data is below:

Assuming the researcher wants to know whether the performance was different in these groups (alpha = .05).  What is the Sum of Squares Between (SS_B)?  Round to two decimal places.

a.

We have these hypotheses:

H0: the amount of active ingredient in a pharmaceutical pill is 5 mg

H1: the amount is below 5 mg

We can take a random sample of 40 such pills and find the amount of active ingredient in them, and let the sample average be x-bar. We also know that the standard deviation of the amount of active ingredient is 0.3 mg.

If H0 is right, what is the (approximate) distribution of  ?

b.

A supermarket claims that the average wait time at the checkout counter is less than 9 minutes.  Assume that we know that the standard deviation of wait times is 2.5 minutes.

Consider

H0: mu >= 9

H1: mu < 9

A random sample of 50 customers yielded an average wait time of 8.5 minutes.

What is the p-value for this data?

(Provide four decimal places)-----------------

c.  

A supermarket claims that the average wait time at the checkout counter is less than 8 minutes.  Assume that we know that the standard deviation of wait times is 2.5 minutes. We will test at a significance level of 10%.

Consider

H0: mu >= 8

H1: mu < 8

A random sample of 50 customers yielded an average wait time of 7.8 minutes.

What is the critical value for the Zstat (the Z-test statistic)?

(Provide two decimal places)

d.

A manager is looking at the number of sick days used by employees in a year.

H0: the average number is 8 or below

H1: the average is over 8

We know that the standard deviation of the number of sick days used by employees is 2, and we want to test at 10% significance level.

Say we took a random sample of 50 employees, and checked their records, and found that the average was 8.1

The manager figures that the critical value (z-sub-0.1) is 1.28.

What should be the decision?

Height vs Weight - Erroneous Data: You will need to use software to answer these questions.

Below is the scatterplot and corresponding data for the height and weight of 11 randomly selected adults. You should notice something odd about the last entry.

You should be able copy and paste the data by highlighting the entire table.

Answer the following questions regarding the relationship.

(a) Using all 11 data pairs for height and weight, calculate the slope and y-intercept of the regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place.
ŷ =  x +

(b) Using the regression equation from part (a), estimate the weight of a person who is 62 inches tall. Round your answer to one decimal place.
ŷ =  pounds

(c) Using only the first 10 data pairs for height and weight, calculate the slope and y-intercept of the regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place.
ŷ =  x +

(d) Using the regression equation from part (c), estimate the weight of a person who is 62 inches tall. Round your answer to one decimal place.
ŷ =  pounds

(e) Which statement(s) explain this situation?

The height for the last data pair must be an error.The erroneous value from the last data pair drastically changed the regression equation.    Including the last data pair made the slope closer to zero.The prediction from part (d) should be more accurate than the prediction from part (b).All of these are valid statements.

Pretend you are a Shark Tank advisor. Two business partners have come to you for advice for a business they own and operate. This assignment requires you to create a one-page executive summary (not including backup tables of your analysis) of your advice for this business.

Topic/Question - Read the following scenario then address the recommendation/advice section of this assignment.

Tired of hiring themselves out and abiding by corporate rules and various personality issues with management of fitness facilities, two fully certified personal trainers opened a fitness facility. Each trainer was certified in indoor cycle (aka Spinning), personal training, strength, high-intensity training, and TRX. The facility was housed in the finished basement of one owner’s personal residence. They invested $3000 that covers startup equipment costs. Startup equipment included spin bikes, fans, weights, step benches, and mats. Over time they upgraded the spin bikes and added more features such as resistance bands, ropes, TRX equipment, kettlebells and other items for approximately $1000. Based on periodic feedback from clientele, they added some yoga classes and another instructor to teach additional spin classes. The owners taught 90% of the classes themselves and did not take a salary from the business. The yoga classes fully funded the yoga instructor. The additional spin instructor cost approximately $150/month. Costs included $500 monthly for insurance, $200 monthly for utilities, $80 for music licensing. Clientele paid $10 per class unless they purchased a package of 20 classes for $85 or 10 classes for $65. They ran approximately 26 classes a week. Unless there were 2 clients in a class, the class was cancelled. The business averaged 4 clients per class and averaged cancelling 3 classes per week. They also had personal training clients who paid 20 per session. The business averaged 8 personal training sessions per week. Tax rate is 20%. Depreciation on the equipment is 20% a year. Efficiency of the business is compromised from time to time based on clientele – since this is a boutique business that runs classes of 5-6 individuals, personalities and drama sometimes require the business owner’s significant management time in the form of communications with clientele.

Between the two of them, they could earn $800/month by contracting themselves out to other facilities. Additionally, without the business, the trainers could conduct personal training sessions in the basement facility using the equipment they already have and would incur insurance costs of $60/month, no music licensing fees and $100 utilities.