10. The director of the project wants to test if the weight of wood needed for cooking with the improved stove is significantly less than the weight of wood needed for cooking with the old stove.

A. What are the appropriate hypotheses for this test? Note: Consider the intended test in context of the reduction variable.

B. Based only on the previous parts, which of the following options is true for the value of the p-value for this test? a. The p-value is less than 0.05. b. The p-value is less than 0.10. c. The p-value is greater than 0.05. d. The p-value is greater than 0.10.

C. Based only on the previous parts, is there sufficient evidence to reject the null hypothesis at the 10% level of significance? Explain.

D. Based only on the previous parts, state the appropriate conclusion of the test in context.

E. Interpret the level of significance, α = 0.1, in context.

F. What is the power of this test using the pilot study design to detect an improvement of 0.3 kg? G. Based on the result from part F., what is the probability of a Type II error? please help!

You may assume that the conditions needed for inference to be reliable are satisfied. You may assume (based on many similar studies) that the population standard deviation of reduction of firewood used is 0.7 kg

****URGENT******

1A)  An event has four possible outcomes, A, B, C, and D. All of the outcomes are disjoint.

Given that P(B^c) = 0.2, P(A) = 0.1, and P(C) = 0.3, what is P(D)?

1B) A study was conducted on a potential association between drinking coffee and being diagnosed with clinical depression. All 18,832 subjects were female. The women were free of depression at the start of the study in 1996. Information was collected on coffee consumption and the incidence of clinical depression during the ten-year study period.

Are the following events independent?

Event LC: The event of drinking less than or equal to 1 cup of coffee per week

(Little Coffee = LC)

Event D: The event of a diagnosis of clinical depression

(Depression = D)

Round your calculations to four decimal places (or fewer) at each step.

There are multiple ways to test for independence. All involve the comparison of observed and expected probabilities based on probability theory.

In this context:

If the two probabilities are similar (identical to two decimal places), this is evidence of independence.

If the two probabilities are not similar (not identical to two decimal places), this is evidence of a lack of independence.

C) What do your results in (b) tell us, about the ways in which drinking very little coffee (0-1 cups per week) influences, or does not influence, the probability of depression for women in the study population?

Cost Formulas Shorewood Manufacturing produces a single product requiring the following direct material and direct labor:

Description | Cost per unit of Input | Required Amount per Unit of Product

Material A $8/pound 10 ounces

Materia B $5/pound 8 ounces

Material C 20/gallon 0.3 gallon

Cutting labor 9/hour 30 minutes

Shapping labor 11/hour 15 minutues

Finishing labor 12/hour 45 minutes

Manufacturing overhead consits of indirect material, $0.60 per unit of product; indirect labor, $1,000 per month plus $0.70 per unit of product; factory maintenance, $14,000 per year plus $0.55 per unit of product; factory depreciation, $15,000 per year; and annual factory property taxes, $8,000. Selling and administrative expenses include the salaries of a sales manager, $30,000 per year; an office manager, $18,000 per year; and two salespersons, each of whom is paid a base salary of $11,000 per year and a commission of $3 per unit sold. Advertising and promotion of the product are done through a year- round media package program costing $1,000 per week.

Required

a. Analyze all cost and expense factors to determine a general formula (based on units of production) for total cost.

b. Assuming a relevant range of 10,000 to 20,000 units, what is the estimated unit cost for producing and selling 10,000 units? 20,000 units? Explain the variation in unit cost at the two levels of production.

c. If 15,000 units are produced and sold in a year, what selling price results in a net income before income tax of $60,000?

The equation of a regression line, unlike the correlation, depends on the units we use to measure the explanatory and response variables. Here is the data on percent body fat and preferred amount of salt. Preferred amount of salt x 0.2 0.3 0.4 0.5 0.6 0.8 1.1 Percent body fat y 19 31 22 29 39 24 31 In calculating the preferred amount of salt, the weight of the salt was in milligrams. (a) Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in milligrams. (Round your answers to one decimal place.) ŷ = + x (b) A mad scientist decides to measure weight in tenths of milligrams. The same data in these units are as follows. Preferred amount of salt x 2 3 4 5 6 8 11 Percent body fat y 19 31 22 29 39 24 31 Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in tenths of milligrams. (Round your intercept to one decimal place and your slope to two decimal places.) ŷ = + x (c) Use both lines to predict the percent body fat from preferred amount of salt for a child with preferred amount of salt 0.9 when weight is measured in milligrams, which is the same as 9 when weight is in tenths of milligrams. (Round your answers to one decimal place.) in milligrams % body fat in tenths of milligrams % body fat Are the two predictions the same (up to any roundoff error)? Yes No

Question 2: Input price and input efficiency variances

The budgeted and actual data for direct materials and labor are as follows:

Actual sales volume is 100 units. Budgeted sales volume is 80 units.

a) Without computations, characterize the following variances as favorable or unfavorable:
input price variance for DM F U

input efficiency variance for DM F U

input price variance for DL F U

input efficiency variance for DL F U


b) Compute the input price and input efficiency variances for DM and DL.
As a preliminary step, compute actual input quantity (total pounds or hours we actually used) and flexible budget input quantity (total pounds or hours we should have used for actual output):
    actual input quantity for DM =  pounds
    flexible budget input quantity for DM =  pounds
    actual input quantity for DL =  hours
    flexible budget input quantity for DL =  hours
Next, compute the variances. Enter favorable variances as a positive number and unfavorable variances as a negative number. Do NOT enter F or U.
    input price variance for DM = $
    input efficiency variance for DM = $
    input price variance for DL = $
    input efficiency variance for DL = $

Program C You are given some data from an animal shelter, listing animals that they currently have. They have asked you to write a program to sort the dogs and cats in age in ascending order, respectively, and write them in separate files. Assume the input file has the format of name (one word), species (one word), gender (one word), age (int), weight (double), with each animal on a separate line:

Hercules cat male 3 13.4

Toggle dog female 3 48

Buddy lizard male 2 0.3 ….

Example input/output:

Enter the file name: animals.txt

Output file name: sorted_dogs.txt sorted_cats.txt

1. Name your program animals.c.

2. The output file name should be sorted_dogs.txt and sorted_cats.txt. Assume the input file name is no more than 100 characters.

3. The program should be built around an array of animal structures, with each animal containing information of name, species, gender, age, and weight. Assume that there are no more than 200 items in the file. Assume the name of an animal is no more than 100 characters.

4. Use fscanf and fprintf to read and write data.

5. Your program should include a sorting function so that it sorts the animals in age. You can use any sorting algorithms such as selection sort and insertion sort. void sort_animals(struct animal list[], int n);

6. Output files should be in the format of name gender age weight, with 2 decimal digits for weight.

For example,

Toggle female 3 48.01

Rocky male 5 52.32

(a) Chau’s electric circuit is a simple electronic circuit that can exhibit chaotic behaviour. The voltages x(t) and y(t), and current z(t), across components in the circuit can be investigated using the Matlab command

[t,xyz] = ode45(@ChuaFunction,[-10 100],[0.7 0.2 0.3]);

and the function:

1 function dxyzdt = ChuaFunction(~,xyz)

2 % xyz(1) = X, xyz(2) = Y, xyz(3) = Z

3 4 dxdt = 15.6*(xyz(2) - xyz(1) + 2*tanh(xyz(1)));

5 dydt = xyz(1) - xyz(2) + xyz(3);

6 dzdt = -28*xyz(2); 7

8 dxyzdt = [dxdt dydt dzdt]’;

9 end

(i) What is the differential equation involving x˙(t)? Here a dot represents differentiation with respect to time t.

(ii) What is the initial condition for the variable y(t)?

(iii) What does the apostrophe after the square brackets in line 8 of the function signify and why is the apostrophe needed here?

(b) For a given function u(t), explain how the derivative of u(t) with respect to t can be approximated on a uniform grid with grid spacing ∆t, using the one-sided forward difference approximation

du/dt ≈ Ui+1 − Ui/ ∆t ,

where ui = u(ti). You should include a suitable diagram explaining your answer

(c) Using the one-sided forward difference approximation from part (b) and Euler’s method, calculate the approximate solution to the initial value problem

du/dt + t cos(u) = 0, subject to u(0) = −0.2,

at t = 0.4, on a uniform grid with spacing ∆t = 0.1.

PYTHON (BEGINNER) program that allows the user to choose any of the three sports options described below and computes the relevant statistic in each case:

Quidditch Score Total: Determined based on the number of goals and whether or not the snitch was caught. A goal is scored by propelling the quaffle through a hoop and each earns the team 10 points. If a team catches the snitch, that team earns an additional 30 points. The snitch can be caught at most once. More details on Quidditch available from the International Quidditch Association.

(Simplified) Quarterback Rating: Defined as

100 * [5(completions/attempts – 0.3) + 0.25(passing_yards/attempts-3) + 20(touchdown_passes/attempts) + 2.375 – (25 * interceptions/attempts)]/6,

where attempts is the number of passing attempts made, completions is the number of completed passing attempts, touchdown_passes is the number of passes for a touchdown, and interceptions is the number of times the ball was intercepted. A perfect passer rating in the NFL is considered to be a 158.3. In addition to the rating, tell the user whether or not the quarterback is a perfect passer.

Gymnast Score: Begins with six scores, one for difficulty and five for execution, each between 0 and 10. Of the execution scores, the highest and lowest are dropped. The final score is given by the sum of the difficulty score and the average of the three remaining execution scores.

Input Validation:

Check if you are going to divide by zero when relevant, and do not do the calculation if that is the case.
Before typecasting user inputs to an int, check that it is only digits, and don’t typecast or do the calculation otherwise. (For this assignment, do not worry about checking if floats are valid.)
In any case where an error is detected, output an error message. Do not continue the calculation. You may additionally output a result of zero in such a case.

Selected ratios for 2018 for two companies in the same industry are presented below:

REQUIRED: Answer each of the following questions providing the ratio(s) to support your answer, explain.

1) Comment on how successful each company appears to managing its accounts receivable. Terms are net 30 for both companies
2) How well does each company appear to be managing its inventory?
3) Which company is more solvent, explain using ratios?  
4) Which company is more profitable, explain using ratios?
5) The gross profit margin for Draco is higher than Potter's and the industry average. Provide two reasons why this would be the case?
6) Which company would investors believe would have greater prospects for seeking growth?
7) Why is Basic Earnings per Share not comparable between companies?