One of the potential problems with supplementing endangered wild populations with captive bred individuals is that captive bred organisms often have reduced fitness compared to their wild counterparts. Reasons for this are varied, but work suggests it is a combination of reduced genetic variation in captive bred populations (small population sizes and assortative mating leading to reduced genetic variation) as well as reduced fitness due to individuals adapting to a captive environment as opposed to a wild environment. Fundy Atlantic salmon (Salmo salar) are an endangered salmon species whose numbers have declined to a point that scientists started to supplement their wild numbers with captive bred individuals. The question you will answer here is: is supplementing wild salmon populations with captive-bred individuals beneficial if the captive bred individuals have lower fitness than the wild population?

The average number of eggs laid by females in the wild population is about 2,500/female. The captive bred individuals typically exhibit about 30% lower fecundity than wild individuals (some estimates are up to 40% lower, but we will use 30% for purposes of this assignment).

1. If the heritability of fecundity is 0.1, what do you predict the fecundity of the new population will be (assume you add just as many new individuals as were already in the wild population)? (2 points)

2. Now consider if the heritability of fecundity was higher, let’s say 0.3 Now what do you predict the fecundity of the new population will be (using all the original numbers, not after one generation of selection)? (2 points)

3. If fecundity exhibits high heritability, what do you predict will happen to population numbers in this population over time if captive bred individuals are added every year (2 point)?

Lucky Restaurant makes and sells a variety of soups. It also makes and sells whole-grain bread. It anticipates the following financial performance for its bread business during the month of May.

Lucky's management expects its selling price, variable cost per unit, and total fixed cost to remain the same for next year.

Required:

Question 1:

Lucky received a special order for 4,000 loaves of bread. The loaves are identical to the loaves it currently produces. However, because the order is a special order, it will not need to pay the $0.20 per loaf commission to its sales force.  Compute the minimum price per loaf that it should charge for the special order.

Question 2:

Management is considering whether to outsource the production of bread for the months of June and July so that its baker can take a two-month vacation. It believes that outsourcing will not affect bread sales and that bread sales will be the normal 22,000 loaves per month for June and July.

Management has gathered the following information about outsourcing:

• Whole Earth Breads will sell the bread to Lucky for $2.00 per loaf
• If bread production is outsourced, Lucky will be able to save a total of $8,800 in fixed costs($4,400 in June and $4,400 in July)

Compute the most Lucky should be willing to pay per loaf to purchase the break from Whole Earth Breads.

Suppose the manufacturer of a certain drug claims the adverse event rate of the drug is 20% (ie. 20% of people who take the drug have an adverse event), but you think the adverse event rate is higher. (In fact, you think the adverse event rate is 30%.) So, you want to do a study to show the adverse event rate is higher than 20%. If the adverse event rate is really 30% and you obtain a sample of size 10 patients, what is the power of your study for testing Ho: p=0.2 vs Ha: p > 0.2 with a significance level of 0.05? To address this question, answer the following: a) State in words what "power" means in the context of this problem. b) Determine the minimum number of adverse events among 10 patients that would need to happen to reject your null hypothesis. In other words, determine the minimum number of adverse events so that the one-sided p-value is less than 0.05. c) Now, calculate the probability of observing the number of events from part b or more events under the assumption that the true rate is 30%. In other words, calculate the power (the probability of rejecting the null hypothesis if the adverse event rate is really 0.3). d) Now do steps b) and c) to determine the power if the rate were really 70%. e) (*1 point) Compare the power in c) and d). This comparison illustrates (choose the best answer): i) power is higher with alternatives closer to the null hypothesis. ii) power is higher with alternatives farther from the null hypothesis. iii) power is higher with a smaller Type I error rate. iv) power is higher with a larger Type I error rate.

Study Design and Sample Size

The study is a non- randomized controlled trial including eight intervention and six control schools. The study assessed knowledge, attitudes and behaviors of the students three times over a period of eighteen months: March 2009 (Baseline), March 2010 (TI) and September 2010 (t20. We based the sample size calculation on the study objective of assessing whether or not the intervention influenced the time trend in condom use and recent history of sexual intercourse. Sample size calculations were conducted with Wald tests for odds ratio resulting from regression models with two binary variables (intervention/ control and TO/T1 OR T0/T2) and their interaction. For logistic regression models, a minimum of 1,241 observations are required to detect an adjusted odds ratio of 2 or more with 80% power under conservative assumptions of 30 % baseline prevalence of the outcome variable and no changes over time in the control group. For linear regression models, a minimum of 348observations are required to detect a small standardized effect size (Cohen’s d) of 0.3 with 80% power at the 0.05 significance level. Further, we assumed a design effect of 2, due to possibly strong correlation of repeated measurements from the same participant (TO/TI/T2), resulting in a minimum of 2,482 observations required from 1,241 participants. Anticipating a 25% loss t follow –up. We increased the target sample size to 1,655 participants at TO. Eventually for the research, the target sample was increased from 1,655 to 1950.

Question

The investigators described their sample size calculations, which are relatively complex. Did the investigators achieve the desired sample size? Do you think that the study findings are made stronger or weaker by the size of the sample? Explain your answer.

Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.

1. Formulate a linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. If required, round your answers to two decimal places.

1. What is the optimal solution?

1. What are the values and interpretations of the slack variables?

1. What are the binding constraints?

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 = $