The article “Estimating Population Abundance in Plant Species With Dormant Life-Stages: Fire and the Endangered Plant Grevillea caleye R. Br.” (T. Auld and J. Scott, Ecological Management and Restoration, 2004:125-129) presents estimates of population sizes of a certain rare shrub in areas burnt by fire. The following table presents population counts and areas (in m^2) for several patched containing the plant:

Area	Population	Area	Population
3739	3015	2521	707
5277	1847	213	113
400	17	11958	1392
345	142	1200	157
392	40	12000	711
7000	2878	10880	74
2259	223	841	1720
81	15	1500	300
33	18	228	31
1254	229	228	17
1320	351	10	4
1000	92

1. Create a scatter plot for the two variables, does there seem to be a linear relationship? (Do this scatter plot by hand)
2. Compute the least-square line. (show your work for the sum of squares, slope and intercept)
3. The scatter plot done in part a) is based on the model form y(hat)=a+bx. Create a scatter plot of y versus lnx. What do you notice? (Note: you can find ln y and x using excel, but show your values. Do this scatter plot by hand)
4. In part c), the data is considered to be “transformed”. Of this “transformed” data, compute the least-square line for predicting lny from lnx. (show all your work)
5. In part c), the data is considered to be “transformed”. Of this “transformed” data, calculate the value of Pearson’s correlation coefficient and interpret your value. Also, calculate the value of Pearson’s correlation coefficient of the original data, interpret your result. (show all your work by hand)
6. Calculate the proportion of observed variation in “y” for the original data. Explain your result. (show your work for SSE)
7. Calculate the residuals of this original data using Microsoft Excel (Print off your residual values in excel). Create a residual plot by hand. Comment on your plot.

3. a) What does an income elasticity of demand of +1.33 mean? b) Explain why the government potentially can raise more tax revenue if it applies a tax to a good with inelastic demand than if it applies the tax to a good with elastic demand? c) The Vice Chancellor of a university is concerned about increasing costs, and decides to raise tuition fees in an attempt to increase university revenue. Briefly explain (i.e. 2 or 3 sentences) whether you think this move will accomplish the Vice Chancellor’s objective.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

Day		Revenue			Occupied		Day		Revenue			Occupied
1		$	1,452		60		14		$	1,425		31
2			1,361		20		15			1,445		51
3			1,426		21		16			1,439		62
4			1,470		80		17			1,348		45
5			1,456		70		18			1,450		41
6			1,430		29		19			1,431		62
7			1,354		30		20			1,446		47
8			1,442		21		21			1,485		43
9			1,394		15		22			1,405		38
10			1,459		36		23			1,461		36
11			1,399		41		24			1,490		30
12			1,458		35		25			1,426		65
13			1,537		51

a. Choose the scatter diagram that best fits the data.

b. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

1. c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

d.

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

Scaves

Scaves is one of Scandinavia’s largest furniture manufacturers, and sells their

furniture designs all over Europe and beyond. The company was founded in 1934 in

north-western Norway. From their small base in Sykkylven set amidst deep fjords,

and mountains, the company has gone on to become an international success story.

From these humble origins, the firm has become an international success story, selling

furniture in 19 countries including USA and Japan. The company is famous for its

‘Stressless’ brand of leather recliners. This product range has become the cornerstone

of the company’s success. It sells their extensive furniture range under a number of

different brands such as ‘Stressless’ recliner chairs, the ‘Scaves’ sofa collection,

‘Sbane’ mattresses, and ‘Soko’ beanbags. Scaves uses a variety of different brands to

cater for different markets and consumer segments, but the Scaves name is always

associated with these sub-brands, and the company is always trying to enhance brand

association and awareness. It feels that by consumers seeing the Scaves brand name, it

acts as a sign of great product quality. Scaves has developed into a one of Norway’s

most well known international brands.

Jon Scaves, started the company with three employees, and initially pioneered the

selling of mattresses with springs loaded inside the mattress. This was developed into

the “Sbane” mattress brand. Over 70 years later, this brand continues to be sold.

Gradually the firm expanded their range to include other furniture. Now the firm

encompasses a range of sofas, recliners, ottomans, tables, chairs, mattresses, and other

furniture accessories. It achieved international success and prominence through its

landmark and distinctive recliner designs. Through its history it has experienced highs

and lows, nearly experiencing bankruptcy, and having to face large lay offs. This

evolution has seen the firm use a variety of sales structures, seeing different phases of

expansion and retrenchment. Now the firm is powering ahead, through developing its

international sales, and capitalising on the strength of its recliner range.

Table 1: Scaves at a glance

Headquarters are based in a beautiful mountainous region in Ikornnes, which is an

area called Sykkylven, Norway.

Its slogan - “The Innovators of Comfort”

Founded in 1934.

Has revenue of 2,292 million (NOK) or €282 million in 2005.

Profits of 303 million (NOK) or €37 million

Employs 1,545 staff.

Has a total of seven factories in Norway. The company has invested heavily in state

of the art machinery, including automated robots.

The firm now has the capacity to produce over 2,000 ‘Stressless’ seats a day.

Scaves products are available through a network of furniture dealers in over 19

countries including Germany, UK, France, Russia, Japan, Canada, USA, and Poland.

Over 82% of the firm’s products are destined for foreign markets

Its main vision is to become a leading brand name supplier of home furniture in

domestic and international markets. It believes in offering customers, a great quality

premium product at great value for money. In promoting the range, Scaves uses studio

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merchandising, showcasing a variety of Scaves products in a typical real life setting.

Here samples of the product range are shown to full effect, where prospective buyers

are encouraged to take “the Scaves comfort test”. Scaves designs products with

a focus on comfort, design, and function. Any of the product range has to

entice customers, and make it distinctive from competing furniture ranges, especially

in competing against low cost suppliers. Scaves offers 10-year guarantees on its

internal mechanisms, which is a testament to its quality. The firm uses furniture

designers to come up with new designs that make the range modern and highly sought

after. Similarly, the firm works closely with textile suppliers to ensure their colours,

designs are fashionable for modern consumer tastes. This is particularly important

with the firm’s sofa ranges that can easily date.

The ‘Stressless’ brand is the company’s core brand. It was originally designed back in

1971. Its functional design, unique base support, adjustable headrest, 360 degree

rotation, free standing footstool and overall comfort offered to users proved a winning

combination. The company vigorously defends its unique design, winning copyright

infringement cases against would-be furniture copycats. These recliners are offered in

three sizes, small, medium, and large. One of the main selling points of the

‘Stressless’ recliner is that the chair is highly adjustable to provide maximum lumbar

support and comfort. It uses the strapline of the ‘ultimate recliner’ to support the

‘Stressless’. Furthermore the firm sells a range of ‘Stressless’ accessories to

compliment the recliner such as table attachments, and height adjusters. It offers the

recliners with four different categories of leather, with different finishes, and these

can then be chosen in a wide variety of colours. Scaves customers can choose from

over 50 different leather colours, and 7 different wood grain effects. The level of

customisation is a key selling point that entices would-be customers, and allows the

firm to charge premium prices. These recliners like most of the product range are

priced at the premium end of the market. A recliner can retail for anywhere between

£1,200 (€1,725) and £1,800 (€2,675).

The ‘Stressless’ recliners account for 79% of total sales, the mattress range 9%, the

sofa collection another 9%, while the remainder makes up other Scaves furniture

products. It hopes to break into new markets such as creating suitable furniture for the

home cinema phenomenon, selling a range of sofas and recliners suitable for home

cinema enthusiasts. The company has changed with the times offering a new feature,

called “safe” on certain models allowing the leather upholstery to be removed like a

duvet cover, so that it can be washed and cleaned. The company has also developed

corner and sofa units for its recliner series. These developments have strengthened the

company’s product portfolio, showcasing the ‘Stressless’ brand philosophy.

Its closest comparable competitors in the market are the American famous La-Z-Boy,

and Italian Natuzzi product range. Other recliners are not strongly branded, yet are

sold through well-known large retail chains such as DFS, Argos and Ikea. Some of

these large retail chains have tremendous buying power and market prominence,

selling their own label branded furniture. Many of Scaves competitors are small to

medium sized suppliers, mainly based in Asia. Their distinct advantage is cost. Far

East furniture suppliers have helped drive down furniture prices, and helped

democratise leather furniture. The company envisages that to remain successful, it

must consistently build the brand, invest in product development, and have a strong

distribution network. Through this commitment it can achieve higher margins that

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make its future more sustainable.

To reduce costs Scaves tries to standardise components. It endeavours to garner

economies of scale through large volumes, especially when it competes with low cost

manufacturing sites such as in Far East Asia. Its production philosophy is focused on

continuous quality improvement initiatives, delivery precision, and the optimisation

of the company’s manufacturing resources. In an effort to get greater production

efficiencies, the firm is aiming to reduce the number of models it offers to customers,

whilst achieving higher volume sales on core Scaves products. The company has 32

different ‘Stressless’ recliner models, and 12 different ‘Stressless’ sofa models.

Table 2: The Objectives of Scaves

1. Have a return on total booked assets of min. 25%

2. Have a return on sales of min. 15%

3. Have an asset turnover of min. 1.7 times

4. Have an equity ratio of min. 40 – 50%

5. Have a gross margin in the Stressless business segment of min. 49%

6. Have a gross margin in the Svane business segment of min. 40%

7. Have a gross margin in the Scaves Collection business segment of min. 40%

8. Have an annual growth of 5 – 10%

The company sells its products through selected retail chains and independent

furniture dealers. The company sees further growth in new international markets such

as Italy, Portugal, some Eastern European countries, and Asia. The firm is an export

driven firm with over 82.1% of products exported abroad. The company uses a

network of company owned sales offices to establish a network of specially selected

distributors in foreign markets. Typically retailers include retail chains and

independent furniture dealers. The furniture range is sold exclusively through these

retail dealers, and is not available on the Internet. Scaves believes that customers want

to ‘touch and feel’ furniture before buying it. The tangible nature of furniture buying

is very important. Dealers have samples of different woods and finishes, which

customers can order. The selection of reputable dealers in international markets is

seen as crucial. Dealers are chosen based on suitable geographic distribution

coverage. Scaves view is that they have to form mutually beneficial partnerships with

its dealers that encourage dealer motivation to stock and support Scaves marketing.

Not all of the Scaves range is available internationally. Its truly international brand is

the ‘Stressless’ recliner, with 95% of all ‘Stressless’ recliners being sold in export

markets. Its ‘Sako’ beanbag furniture range specially designed for kids and the

‘Sbane’ mattress is extremely popular in Scandinavian markets, having a 70-year-old

brand heritage.

The company has a presence in over 19 countries. Scaves has even opened

a showroom in Las Vegas. Scaves has a variety of international websites designed to

promote the brand. The look and feel of these websites is generic, yet all the sites

have local content. No prices are published on their website or on dealer websites.

The company encourages dealers to use the Scaves brand on dealer Internet sites

also. The company focuses their marketing strategies on strong point of purchase

displays, and local advertising campaigns in conjunction with their dealer network.

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Building up the distribution base for Scaves internationally is vital. A key activity in

securing greater distribution coverage is forming and cultivating relationships with

dealers. The company uses international furniture fairs to secure new dealers, and

showcase their product range to prospective dealers. The range and number of dealers

vary depending on the international market targeted. For example, to expand in Japan,

Scaves uses a network of 400 dealers, where it directly assumed ownership of the

sales channel, by taking over the activities of an importer who had previous

responsibility. In the USA, there are over 375 furniture dealers with 550 outlets that

stock Scaves. Sales growth for Scaves products is continuing to grow in all

international markets achieving between 5%-10%. However, challenges are on the

horizon including mounting cost pressures, exchange rate fluctuations, pressure on

retailer margins, enhanced competition, and copycat products.

Many international furniture dealers are motivated to stock Scaves due to the

strength of the Scaves brand name, the product range, its heritage, its popularity

within the market, and most importantly its margins! In addition to providing a

dealership contract, Scaves provides dealers with additional training programmes for

retail sales staff, branded marketing material, Internet marketing support, and studio

solutions showcasing the product range. Any marketing activity is designed to

promote Scaves brand identity, and to encourage footfall to their dealer network. Both

the strength of the product and its pricing are important. Scaves feels that an effective

supply chain can help encourage consumer purchase behaviour. Scaves tries to ensure

short lead times for products to be delivered, and that promised lead times are met.

Product is typically flat packed to their dealer network, whereby dealers look after

final assembly and delivery of the product to consumers. Scaves want to create a

reputation as a reputable supplier of furniture. The timely delivery of flawless

products is vital in achieving this reputation. Any complaints are handled as

expeditiously as possible.

Through their advertising the company tries to emphasise – “The Comfort Test”, and

uses the slogan “The Innovators of Comfort”. This is their core positioning strategy,

which has been tremendously successful. Will it continue to yield dividends into the

future?

Q. Develop a marketing objectives, financial objectives, target markets, positioning, strategies, and the marketing mix elements for Scaves.

I, Answer the question following the fact pattern:

A] Warehouse manager knows that the cold season has passed. He still has Winter items that he would like to sell. He offers to retailers:

- coats @75/ea; 40/15 net 30; Retailer purchases 10 coats on June 30th

-gloves @30/pair; 25/15; Retailer purchases 50 pairs of gloves on July 1st

- boots @140/pair 35/5; Retailer purchases 27 pairs of boots on July 5th

*** additional 7 and 1/2% for out of season purchase.

A] Having inspected the bought items Retailer notices that several of them are damaged:

- 3 of the coats; 8 pairs of gloves; 5 pairs of boots. On July 8th When Retailer returns to pay he notices a sign that reads: "All damaged items return for exchange only. If exchange not possible then refund at the per item purchase price". There are no more coats, 6 pairs of gloves are available, only 3 pairs of boots remain. What is Retailer's total bill?

II.   Company is ready to introduce its widget into the marketplace. Only one other comparable widget exists. That widget costs $28. However, Company's widget has several features that the other does not. Research has shown that at least 20% of potential purchasers would really appreciate these features. Company has decided that its widget price can range from $28 to $35. Company decides to sell its widget for $34.99. What pricing strategy (ies) has Company chosen? Explain.

The table below represents 2 attempts that students had to complete the same statistics exam in a course.

Student	Exam- 1st attempt (%)	Exam-2nd attempt (%)
1	59	71
2	64	63
3	86	87
4	74	82
5	83	89
6	52	40
7	57	62
8	38	55
9	31	70
10	74	78
11	70	78
12	64	59
13	40	57
14	55	59
15	70	65

1) The professor believes that, on average, students will do better on the second attempt than on the first.

a) Choose an appropriate test to determine if students improved on the second attempt compared to their first. Draw appropriate conclusions.

b) Calculate the size/magnitude of this effect.

c) Identify the 95% confidence interval around our measurement and explain what this result tells us about our data.

2) I modify the table so that the column labelled 1st attempt now represents the results from students in Prof A’s statistics class, and the column labelled 2^nd attempt represents the results of a completely different group of students taking Prof B’s class.

a) Choose the appropriate test to demonstrate if there is a significant difference in the results in Professor A’s class compared to Professor B.

b) Is my approach to this problem the same as in Question 1). Why or why not?

3) I keep the table changes mentioned in question 2. The 1st attempt column still represents the results from students in Professor A's statistics class and the 2nd attempt column represents different students from Professor B.'s class. Professor A discovers that 3 students in his class cheated so he eliminates their grades from the group. If I now wanted to compare the performance of class A and class B, should the statistical approach change compared to Question 2? Why or why not? (Note: You do not need to do the calculations; you just need to provide an explanation.)

**********************
I'm going to modify the table a bit. Data now represent the marks obtained by students in the statistics course at the mid-term exam and in the final exam in 2018.

Student	Grade in midterm exam (%)	Grade in final exam (%)
1	59	71
2	64	63
3	86	87
4	74	82
5	83	89
6	52	40
7	57	62
8	38	55
9	31	70
10	74	78
11	70	78
12	64	59
13	40	57
14	55	59
15	70	65

4) I would like to know if there is a relationship or link between the grades that the students obtained in the midterm exam and in the final exam.

a) Make an appropriate graphical representation to illustrate these data.

b) What conclusions can we draw only by looking at this graph? Are there any data points that seem problematic?

5) a) What is the strength of the relationship between these two variables?

b) What part of the variance could be explained by the relationship that exists between these variables?

c) Is this relationship statistically significant?

6) In the 2019 winter semester, a student obtained a grade of 64 in her midterm exam. What grade could we predict that she will get in the final exam?

7) a) If I wanted to test the relationship between the midterm exam performance and the final exam using a chi-square test, how would the above data table need be rearranged/modified?

b) Despite my suggestion in 7a) to use a chi-square test, it would actually be a bad idea to use the chi-square test with this type of problem. Why might that be the case? What problem (s) would it cause? (Think of the rules we discussed for using chi-square.)

The first company: preparing the income statement in the short way to the company, and the data is below?

Here is the information for Al-Rafidain Company, which is required to prepare the short-term income statement:

400,000 net sales, 300,000 dividend income, 150,000 rental income, 75,000 consulting revenue, 100,000 cost of goods sold, 35,000 marketing expenses, 30,000 selling expenses, 20,000 administrative expenses, 10,000 maintenance expenses, 10,000 tax expenses

The rate at which customers are served at an airport check-in counter is a Poisson process with a rate of 10.4 per hour. The probability that more than 50 customers are served at the counter in the next 5 hours is P(Xp>50). If this is solved as a Poisson variable, the calculations will be tedious. So we use the normal approximation. Now, P(Xp > 50)=P(Z > a), where Z is the standard normal variable. What is the value of a? Please report your answer in 3 decimal places