Elk, Fire and Aspen – Quaking aspen (Populus tremuloides) is one of the most widespread tree species in North America. Although quaking aspen has been a key component of forest ecosystems for more than ten thousand years, it is currently in decline across broad portions of its range. Historically, aspen recruitment has been favored by the occurrence of low intensity fires, which create openings that allow young aspens to grow and eventually reproduce. In recent decades, however, the number of fires per year and the area burned per fire has increased; these increases in the frequency and magnitude of fires are thought to be caused by the “hotter droughts” that have resulted from climate change and by previous fire suppression policies. Some recent fires have destroyed more than 400 km2 of forest; such fires are referred to as “mega-fires.” In addition to fire, browsing by elk can prevent young aspen trees from becoming large enough to reproduce. Field Experiment – Suppose that researchers wanted to examine the combined effects of a mega- fire and browsing by elk (Cervus elaphus) as factors that may be affecting the decline of quaking aspen. Immediately after a mega-fire, the researchers established fenced-in plots that prevented by browsing by elk (the “Elk absent” treatment) along with nearby plots from which elk were not excluded (the “Elk present” treatment). Five fenced-in plots and five unfenced plots were established in each of two areas: A section of forest that was burned in the mega-fire (the “burned” treatment), and a nearby section of forest that was not burned (the “unburned” treatment). After 6 years, the number and mean height of young aspen trees in each plot are shown in table
1. What is the total number of plots that were established in this experiment? How many of these plots were burned? How many were unburned?
2. The aspen height data were used draw the bar graph shown in Fig. 1. Summarize how elk and fire affect the height of young aspen trees by answering the following questions: 2.1. What are the overall effects of elk and fire on aspen height? 2.2. Does the impact of fire on aspen height depend on whether elk were present?
3. Summarize how elk and fire affect the number of young aspen trees by answering the following questions: What are the overall effects of fire and elk on the number of aspen? Does the impact of elk on aspen number depend on whether the plots were burned? Does the impact of burning on aspen depend on whether elk were present?
| Treatment | Number of Trees | Mean Height |
| Elk absent, burned | 2058 | 2.8 |
| Elk absent, unburned | 738 | 1.2 |
| Elk present, burned | 91 | 0.3 |
| Elk present, unburned | 753 | 0.4 |
In: Advanced Math
If a population does not have a normal distribution, the shape of the corresponding x-bar curve will be
| a. |
exactly normal |
|
| b. |
approximately normal |
|
| c. |
Non-normal |
|
| d. |
depends on the sample size |
1 points
QUESTION 2
Ch7 Terms 5:
As sample size increases, the standard deviation of the x-bar curve
will
| a. |
increase |
|
| b. |
decrease |
|
| c. |
remain unchanged |
|
| d. |
explode |
1 points
QUESTION 3
Ch7 Terms 11 TF:
As sample size increases, the distribution of an xbar curves
becomes more and more normal in shape.
| a. |
TRUE |
|
| b. |
FALSE |
1 points
QUESTION 4
17 term 5:
A sample average is useful because it is identical to the
population average
| a. |
TRUE |
|
| b. |
FALSE |
1 points
QUESTION 5
AInv Prob percentiles 6:
Use your TI83 (or Excel):
A normally distributed population has a mean of 93 and a standard
deviation of 12. Determine the value of the sample average at the
75th percentile for samples of siz 43.
Round to the nearest tenth
2 points
QUESTION 6
sigma xbar 1:
Suppose a sample of 77 healthy adult human body temperatures is
taken from a population with a standard deviation of 0.3 degrees
Fahrenheit. What would be the sampling deviation of the sample
mean?
Round to the nearest thousandth
2 points
QUESTION 7
Prob 6 11B:
Use your TI83 (or Excel):
A certain giant tortoise has a life span that is normally
distributed with a mean age of 72 years and a standard deviation of
19 years. Determine the probability that a random sample of 37 such
tortoises has an average life span between 70 and 81 years.
Round to four decimal places.
2 points
QUESTION 8
Prob 1 11B:
Use your TI83 (or Excel):
A Test has scores that are normally distributed with a mean of 79
and a standard deviation of 14. Determine the probability that a
random sample of 31 test scores has an average greater than
77.
Round to four decimal places.
2 points
QUESTION 9
interval 5:
A normally distributed population has a mean of 90 and a standard
deviation of 19. Sample avergaes from samples of size 13 are
collected. What would be the upper end of the centered interval
that contains 95% of all possible sample averages?
Round to the nearest hundredth
2 points
QUESTION 10
Dinner app 1 ch 11B:
Use your TI83:
At a certain restaurant in Chicago, the average time it takes a
person to eat a nice dinner is 55 minutes with a standard deviation
of 20 minutes. These times are known to be normally
distributed.
To Four decimal places, what is the probability a random diner will
finish dinner in more than 54 minutes?
In: Statistics and Probability
|
{Exercise 16.33} The following exercises require the use of a computer and
software. Dataset:
Fire damage in the United States amounts to billions of dollars, much of it insured. The time taken to arrive at the fire is critical. This raises the question, Should insurance companies lower premiums if the home to be insured is close to a fire station? To help make a decision, a study was undertaken wherein a number of fires were investigated. The distance to the nearest fire station (in kilometers) and the percentage of fire damage were recorded. a) Test to determine whether there is evidence of a linear relationship between distance to the nearest fire station and percentage of damage. Select one of the following: 1) There is evidence of a linear relationship between distance and fire damage 2) There is not enough evidence of a linear relationship between distance and fire damageItem 1 b) Estimate the slope coefficient
with 95% confidence (to 3 decimals). c) Determine the coefficient of
determination (to 4 decimals). d) What does this statistic tell you about the
relationship? 1) There is a weak linear relationship between distance and fire damage 2) There is a moderately strong linear relationship between distance and fire damage 3) There is a very strong linear relationship between distance and fire damage 4) There is no linear relationship between distance and fire damage |
In: Statistics and Probability
Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants.
| Annual Sales Growth (%) and Loyalty Card Usage (%
of Net Sales) (n = 74 restaurants) |
||||||||||||||||||
| Store | Growth% | Loyalty% | Store | Growth% | Loyalty% | |||||||||||||
| 1 | -8.3 | 2.1 | 38 | 7.1 | 1.6 | |||||||||||||
| 2 | -4.0 | 2.5 | 39 | 7.4 | 1.8 | |||||||||||||
| 3 | -3.9 | 1.7 | 40 | 7.7 | 2.2 | |||||||||||||
| 4 | -3.4 | 2.1 | 41 | 7.9 | 2.2 | |||||||||||||
| 5 | -3.3 | 2.5 | 42 | 8.1 | 2.8 | |||||||||||||
| 6 | -1.9 | 3.0 | 43 | 8.3 | 2.4 | |||||||||||||
| 7 | -0.8 | 2.3 | 44 | 8.5 | 3.1 | |||||||||||||
| 8 | -0.4 | 2.3 | 45 | 8.6 | 2.2 | |||||||||||||
| 9 | -0.2 | 2.2 | 46 | 8.7 | 1.3 | |||||||||||||
| 10 | -0.2 | 2.3 | 47 | 8.8 | 1.8 | |||||||||||||
| 11 | 0.5 | 2.1 | 48 | 8.8 | 2.5 | |||||||||||||
| 12 | 0.6 | 2.5 | 49 | 8.9 | 1.9 | |||||||||||||
| 13 | 0.8 | 2.0 | 50 | 9.1 | 2.0 | |||||||||||||
| 14 | 1.9 | 2.0 | 51 | 9.5 | 2.4 | |||||||||||||
| 15 | 2.0 | 2.0 | 52 | 10.2 | 2.2 | |||||||||||||
| 16 | 2.1 | 2.6 | 53 | 10.7 | 2.2 | |||||||||||||
| 17 | 2.8 | 2.2 | 54 | 11.0 | 0.3 | |||||||||||||
| 18 | 2.9 | 2.1 | 55 | 11.3 | 1.9 | |||||||||||||
| 19 | 4.0 | 1.9 | 56 | 11.4 | 1.9 | |||||||||||||
| 20 | 4.0 | 2.2 | 57 | 11.5 | 2.2 | |||||||||||||
| 21 | 4.0 | 0.7 | 58 | 11.7 | 2.6 | |||||||||||||
| 22 | 4.0 | 2.0 | 59 | 11.8 | 2.2 | |||||||||||||
| 23 | 4.2 | 1.8 | 60 | 11.9 | 2.1 | |||||||||||||
| 24 | 4.6 | 2.1 | 61 | 12.5 | 2.0 | |||||||||||||
| 25 | 5.1 | 2.5 | 62 | 12.8 | 0.9 | |||||||||||||
| 26 | 5.1 | 2.6 | 63 | 13.8 | 1.1 | |||||||||||||
| 27 | 5.5 | 2.0 | 64 | 14.1 | 3.4 | |||||||||||||
| 28 | 5.9 | 2.0 | 65 | 14.2 | 1.2 | |||||||||||||
| 29 | 5.9 | 1.4 | 66 | 14.6 | 2.1 | |||||||||||||
| 30 | 6.0 | 2.0 | 67 | 14.9 | 0.9 | |||||||||||||
| 31 | 6.1 | 2.1 | 68 | 15.4 | 2.2 | |||||||||||||
| 32 | 6.1 | 2.1 | 69 | 16.2 | 1.7 | |||||||||||||
| 33 | 6.1 | 2.7 | 70 | 17.2 | 2.4 | |||||||||||||
| 34 | 6.3 | 2.0 | 71 | 18.4 | 2.8 | |||||||||||||
| 35 | 6.6 | 2.0 | 72 | 20.8 | 1.1 | |||||||||||||
| 36 | 6.9 | 1.6 | 73 | 25.5 | 0.6 | |||||||||||||
| 37 | 6.9 | 1.9 | 74 | 28.8 | 1.8 | |||||||||||||
(b) Find the correlation coefficient.
(Round your answer to 3 decimal places. A negative value
should be indicated by a minus sign.)
r
___________
(c-1) To test the correlation coefficient for
significance at α = 0.05, fill in the following. (Use the
rounded value of the correlation coefficient from part b in all
calculations. For final answers, round tcalc to
3 decimal places and the p-value to 4 decimal places.
Negative values should be indicated by a minus
sign.)
| tcalc | |
| p-value |
In: Statistics and Probability
Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants.
| Annual Sales Growth (px;) and Loyalty Card Usage
(px; of Net Sales) (n = 74 restaurants) |
|||||||||||||||||
| Store | Growth% | Loyalty% | Store | Growth% | Loyalty% | ||||||||||||
| 1 | -8.0 | 0.5 | 38 | 7.3 | 2.4 | ||||||||||||
| 2 | -7.5 | 2.5 | 39 | 7.5 | 1.6 | ||||||||||||
| 3 | -6.4 | 2.4 | 40 | 7.8 | 1.9 | ||||||||||||
| 4 | -5.2 | 1.8 | 41 | 8.0 | 2.1 | ||||||||||||
| 5 | -5.0 | 2.1 | 42 | 8.1 | 1.6 | ||||||||||||
| 6 | -1.7 | 1.6 | 43 | 8.1 | 1.3 | ||||||||||||
| 7 | -0.7 | 2.1 | 44 | 8.5 | 2.5 | ||||||||||||
| 8 | -0.5 | 2.2 | 45 | 8.5 | 2.3 | ||||||||||||
| 9 | -0.5 | 1.2 | 46 | 8.6 | 1.4 | ||||||||||||
| 10 | -0.5 | 2.6 | 47 | 8.7 | 0.8 | ||||||||||||
| 11 | 0.3 | 2.6 | 48 | 8.8 | 2.7 | ||||||||||||
| 12 | 0.9 | 0.8 | 49 | 9.0 | 2.1 | ||||||||||||
| 13 | 0.9 | 1.9 | 50 | 9.1 | 1.4 | ||||||||||||
| 14 | 1.2 | 1.3 | 51 | 9.2 | 2.1 | ||||||||||||
| 15 | 1.7 | 2.2 | 52 | 10.5 | 2.0 | ||||||||||||
| 16 | 1.8 | 2.4 | 53 | 10.8 | 1.7 | ||||||||||||
| 17 | 1.9 | 2.5 | 54 | 10.8 | 1.4 | ||||||||||||
| 18 | 2.0 | 1.9 | 55 | 11.0 | 0.9 | ||||||||||||
| 19 | 4.0 | 0.8 | 56 | 11.3 | 1.8 | ||||||||||||
| 20 | 4.3 | 2.1 | 57 | 11.4 | 1.2 | ||||||||||||
| 21 | 4.5 | 1.4 | 58 | 11.6 | 0.7 | ||||||||||||
| 22 | 4.7 | 2.2 | 59 | 11.8 | 1.5 | ||||||||||||
| 23 | 4.9 | 1.5 | 60 | 11.8 | 2.1 | ||||||||||||
| 24 | 5.2 | 1.8 | 61 | 13.5 | 1.2 | ||||||||||||
| 25 | 5.2 | 2.4 | 62 | 14.1 | 1.5 | ||||||||||||
| 26 | 5.3 | 1.6 | 63 | 14.3 | 1.9 | ||||||||||||
| 27 | 5.4 | 1.2 | 64 | 15.1 | 0.7 | ||||||||||||
| 28 | 5.5 | 2.0 | 65 | 15.5 | 2.1 | ||||||||||||
| 29 | 5.6 | 2.6 | 66 | 15.9 | 1.6 | ||||||||||||
| 30 | 5.7 | 2.0 | 67 | 16.0 | 0.9 | ||||||||||||
| 31 | 5.9 | 1.5 | 68 | 16.2 | 2.6 | ||||||||||||
| 32 | 6.0 | 1.9 | 69 | 16.2 | 1.4 | ||||||||||||
| 33 | 6.4 | 2.3 | 70 | 17.8 | 2.2 | ||||||||||||
| 34 | 6.4 | 0.6 | 71 | 18.8 | 2.1 | ||||||||||||
| 35 | 6.6 | 1.9 | 72 | 18.9 | 1.3 | ||||||||||||
| 36 | 6.6 | 2.3 | 73 | 19.8 | 0.6 | ||||||||||||
| 37 | 6.7 | 1.2 | 74 | 24.0 | 1.7 | ||||||||||||
(b) Find the correlation coefficient.
(Round your answer to 3 decimal places. A negative value
should be indicated by a minus sign.)
r
_________
(c-1) To test the correlation coefficient for
significance at α = 0.01, fill in the following.
(Use the rounded value of the correlation
coefficient from part b in all calculations. For final answers,
round tcalc to 3 decimal places and the
p-value to 4 decimal places. Negative values should be
indicated by a minus sign.)
| tcalc | |
| p-value | |
In: Statistics and Probability
|
Stocks A and B have the following probability distributions of expected future returns:
|
In: Finance
Stocks A and B have the following probability distributions of expected future returns:
| Probability | A | B |
| 0.3 | (13%) | (30%) |
| 0.2 | 3 | 0 |
| 0.1 | 11 | 20 |
| 0.2 | 22 | 25 |
| 0.2 | 36 | 41 |
Calculate the expected rate of return, , for Stock B ( = 9.40%.)
Do not round intermediate calculations. Round your answer to two
decimal places.
%
Calculate the standard deviation of expected returns,
σA, for Stock A (σB = 27.07%.) Do not round
intermediate calculations. Round your answer to two decimal
places.
%
Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.
Is it possible that most investors might regard Stock B as being less risky than Stock A?
Assume the risk-free rate is 2.0%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to two decimal places.
Stock A:
Stock B:
Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?
In: Finance
|
The Canadian dollar strengthened against its U.S. counterpart on Tuesday as oil prices rose to 3-1/2-year highs and domestic manufacturing data supported the view that the Bank of Canada will hike interest rates next week. At 4 p.m. EDT, the Canadian dollar was trading 0.4 per cent higher at $1.3138 to the greenback, or 76.12 U.S. cents. The currency traded in a range of $1.3133 to $1.3207. Growth in the Canadian manufacturing sector accelerated in June to its fastest pace in more than seven years, data showed. The IHS Markit Canada Manufacturing Purchasing Managers’ Index rose to a seasonally adjusted 57.1 last month from 56.2 in May. Strengthening of domestic data has come despite slow-moving talks to revamp the North American Free Trade Agreement and a trade dispute with the United States. The White House said on Monday that Canada’s decision to enact tariffs on $16.6-billion worth of American goods in retaliation for U.S. tariffs on imports of Canadian steel and aluminum would not help its economy. “We have been climbing the wall of worry since April and the manufacturing sector in Canada is still posting multi-year strength levels,” said Michael Goshko, corporate risk manager at Western Union Business Solutions. “The Bank of Canada has got to pay attention to something like that.” Perceived chances of an interest rate hike at the July 11 announcement have jumped to nearly 80 per cent from about 50 per cent before hawkish comments by Bank of Canada Governor Stephen Poloz at a news conference last week. On Friday, when domestic data showed a surprise expansion of the domestic economy in April and business optimism, the loonie touched its strongest in two weeks at $1.3131. U.S. crude oil futures settled 0.3 per cent higher at $74.14 a barrel. Oil is one of Canada’s major exports. The U.S. dollar fell nearly 0.5 per cent against a basket of major currencies ahead of the July 4 Independence Day holiday, while stocks on Wall Street were pressured by declines for technology stocks. Canadian government bond prices were higher across a flatter yield curve, with the two-year up 2.5 Canadian cents to yield 1.898 per cent and the 10-year rising 22 Canadian cents to yield 2.142 per cent. The 10-year yield touched its highest intraday level since June 18 at 2.204 per cent. Canada’s employment report for June and trade data for May are due out on Friday. Relating your argument to the material we have covered in the class and using the information about the situation in the Canadian economy from the article, explain why it is expected that Bank of Canada will be increasing the interest rate soon. |
In: Economics
Total marks: 50, plus 10 bonus marks for an answer in PLAN/DO/REPORT format.
An Elevating Business. The annual global market for selling elevators is worth $40bn and the annual global market for maintaining them is also worth $40bn. Just 5 companies have 80% of the market for sales: Kone, Otis, Schindler, Thyssenkrupp and Hitachi, however they have only 40% of the market for maintenance since a large number of small companies maintain elevators even though they don’t sell them. Thyssenkrupp is one of the most innovative elevator suppliers, having recently developed technology that allows elevators to move sideways and well as up and down. Another major innovator is Kone that has recently developed extra strength cables which allow very long travel heights, suited to new buildings over 100 stories high in Asia and the Middle East.
Thyssenkrupp is considering selling its elevator division, to cover financial problems in other divisions of the company. You are a financial analyst, assessing the probability of Thyssenkrupp’s elevator division being sold and to whom and also assessing the revenues if it is sold. Based on your experience in the elevator business, you estimate the following probabilities.
The probability of global sales increasing by > 2% next year is 0.25; and the probability of global maintenance revenues increasing by > 2% next year is 0.2. If at least one of these markets increases by > 2% next year, Thyssenkrupp will not sell its elevator division.
If Thyssenkrupp does want to sell, it could plan on selling to:
a private equity company with a probability of 0.35. This would bring a quick infusion of cash to Thyssenkrupp to assist its other divisions,
Kone, with a probability of 0.45, resulting in a very large and innovative company,
Otis, Schindler or Hitachi with a probability of 0.2.
If Thysennkrupp wants to sell to Kone, the deal may be prevented
by European regulators with a probability of 0.65, since it would
result in a single very large European elevator company which could
constitute a monopoly.
(a) (20) Draw a probability tree to represent the above
situation.
(b) (5) Which method of probability assessment was used to estimate
the above probabilities?
(c) (10) What is the probability Thyssenkrupp does actually sell
its elevator division to Kone?
(d) (15) You estimate that if Kone buys Thyssenkrupp’s elevator
division the revenues will be as follows:
| Mean ($bn) | Standard deviation ($bn) | |
| Kone revenue from sales of new elevators | 7.9 | 1.8 |
| Kone revenue from maintenance contracts | 3.7 | 0.6 |
| Thyssenkrupp revenue from sales of new elevators | 5.6 | 1.2 |
| Thyssenkrupp revenue from maintenance contracts | 2.1 | 0.3 |
What is your estimate of the mean and standard deviation of the
total revenues of the combined company assuming that Kone buys
Thyssenkrupp’s elevator division?
In: Statistics and Probability
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:
| Flexible Budget | Actual | ||||||
| Sales (3,000 pools) | $ | 179,000 | $ | 179,000 | |||
| Variable expenses: | |||||||
| Variable cost of goods sold* | 33,390 | 44,540 | |||||
| Variable selling expenses |
11,000 |
11,000 | |||||
| Total variable expenses |
44,390 |
55,540 | |||||
| Contribution margin |
134,610 |
123,460 | |||||
| Fixed expenses: | |||||||
| Manufacturing overhead | 50,000 | 50,000 | |||||
| Selling and administrative | 75,000 | 75,000 | |||||
| Total fixed expenses |
125,000 |
125,000 | |||||
| Net operating income (loss) | $ | 9,610 | $ |
(1,540 |
) | ||
*Contains direct materials, direct labor, and variable manufacturing overhead.
Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to “get things under control.” Upon reviewing the plant’s income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:
| Standard Quantity or Hours |
Standard Price or Rate |
Standard Cost | ||||
| Direct materials | 3.6 pounds | $ |
2.00 |
per pound | $ | 7.20 |
| Direct labor | 0.5 hours | $ |
6.60 |
per hour | 3.30 | |
| Variable manufacturing overhead | 0.3 hours* | $ |
2.10 |
per hour |
0.63 |
|
| Total standard cost per unit | $ | 11.13 | ||||
*Based on machine-hours.
During June, the plant produced 3,000 pools and incurred the following costs:
Purchased 15,800 pounds of materials at a cost of $2.45 per pound.
Used 10,600 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)
Worked 2,100 direct labor-hours at a cost of $6.30 per hour.
Incurred variable manufacturing overhead cost totaling $3,000 for the month. A total of 1,200 machine-hours was recorded.
It is the company’s policy to close all variances to cost of goods sold on a monthly basis.
1a. Compute the following variances for June, materials price and quantity variances.
1b. Compute the following variances for June, labor rate and efficiency variances.
1c. Compute the following variances for June, variable overhead rate and efficiency variances.
(Do not round your intermediate calculations. Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.)
Show less
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Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.)
|
In: Accounting