Business Analytics In Context : An Introduction To Methodologies 1st Edition Gareth Woods - Solutions

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List five data analytics tools. Explain in detail how any one of these tools is used by companies to analyse Big Data.
Explain how companies can use Big Data to manage risks and detect fraud. Which industry is the most likely to be impacted by these risks and why?
Outline the different techniques used in transforming data.
What are the steps involved in the discovery phase of the data analytics life cycle? How does this step help identify and prepare data for analysis?
Identify and discuss the different techniques that businesses use to analyse Big Data.
Explain how the characteristics of Big Data assist companies in gather- ing Business Intelligence. Also, discuss how it can be overwhelming for SMEs.
Discuss the characteristics of Big Data. Explain how these characteristics have changed and the mechanisms that companies are implementing to adapt to these changes.
What is data visualisation? Give three uses of data visualisation.
What is the sequential patterns data mining technique? Give two exam- ples of its business application.
List and explain three primary classification methods in data mining.
List five types of data mining techniques and explain each of them
What is data exploration, and what is the business value of the data ex- ploration process?
What is the value of data mining in business? Give at least one example.
List the factors influencing data visualisation. Then, discuss in detail any three of these factors outlining their contributions to businesses.
How are classification methods used to assist companies with data mining?
Describe the different approaches to pattern recognition.
How do companies use pattern recognition in data mining?
The first step in the data mining process is data exploration, discuss how is it used to shift through Big Data.
List and explain the components of data science.
What is the difference between structured and unstructured data?
What are the categories of data?
Explain the relationship between data, information, and knowledge.
List and explain the three types of knowledge and give an example for each.
In the context of data analytics, what is information?
Explain when data becomes information.
What is data?
Discuss the different phases of data science.
2. Your sales for a product have plateaued at 25,000 units per week. You decide to run an advertising campaign to increase sales. You keep a record of how much you spend on advertising over a period of 8 weeks. You record the following data:Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8
1. It is known that your age is a significant factor in determining your car insurance renewal price/premium. The table below shows the average insurance premium and the average insurance claim grouped by age.Age Average Premium (£) Average Claim (£)18 − 20 950 3,400 21 − 25 840 3,200 26 −
2. You are the owner of a high end electronics store. To try and increase the number of sales of higher priced goods you have introduced an interest free finance scheme.(a) You have noticed that within the first year of offering the interest free finance that there was an average of 4 loan
1. You have done some market research to determine whether it would be worthwhile launching your new product in a new territory. You have found from your market research that 40% of the people in that territory live in the city centre, 52% live in the suburbs and the rest live in the countryside.
2. You are investigating setting up a coach service between London and Cornwall. Each coach has a maximum capacity of 52 passengers and each coach trip incurs a fixed cost of £780 (regardless of the number of passengers). In addition to these fixed costs there is an additional cost of £30 per
1. You are a telephone sales representative. You are paid £8.50 per hour for a 36 hour week plus a flat commission rate of 4% on total sales:(a) Using the variable x to represent the total weekly sales (in pounds), write down the function W (x) for your earnings for one week.(b) How much would you
2. (a) P (Q) = −2Q3 + 2Q2 + 2Q + 8(b) 100 units with a mximum profit of £10,000(c) dC dw= 9, 372
1. (a) P(Q) = −Q3 − Q2 + 24Q + 4(b) 2515 units with a maximum profit of £42,126.83(c) dC dQ= 478, 406
2. Consider the relationship between revenue R (in thousands) and output Q (in hundreds)which are related by R(Q) = 14Q − Q2 . The total cost function is:C(Q) = 2Q3 − 3Q2 + 12Q − 8.(a) Write down the function relating profit P and output Q.(b) What would your output need to be to maximise
1. Consider the relationship between revenue R (thousands of pounds) and output Q (thousands of units) which are related by R(Q) = 30Q − 3Q2. The total cost function is:C(Q) = Q3 − 2Q2 + 6Q − 4.(a) Write down the function relating profit P and output Q.(b) What would your output need to be to
1. The expression for the total profit is given by:profit = x × Q(x) − C(x) = x × (100 − 0.01x) − (50x + 10,000) = −0.01x2 + 50x − 10,000 To maximise the profit we are required to differentiate the function and set the derivative equal to zero, i.e.−0.02x + 50 = 0 and we find:x =50
1. You have determined that the demand equation for a particular item is given by:Q(x) = 100 − 0.01x with the cost function given by:C(x) = 50x + 10,000 where x is the number of items sold. Calculate the value of x that will maximise the profit and determine the corresponding total profit.
1. You have been asked to report the sales of a particular item to your investors. The data is as follows:Month Sales January 1,687 February 1,547 March 1,498 April 1,589 May 1,601 June 1,702 July 1,731 August 1,689 September 1,581 October 1,891 November 1,901 December 1,801(a) Represent the data
1. (a) We assume that the probability is binomially distribution, i.e. with n = 12 and p = 0.2.The probability of half your team being off sick is given by:12C6 × 0.26 × (1 − 0.2)6 = 0.016(b) You are taking on an additional 8 members of staff who each earn £1,800 × 3 = £5,400 for three
1. You are the owner of your own business with 12 employees.(a) Due to a worldwide pandemic the probability of a member of staff being off sick is p= 0.2. What is the probability that half your team will be off sick at the same time.(b) Due to the number of staff being off sick you are required to
1. You record the selling price of an item and the quantity during each quarter and create the following data set.Selling Price (Pounds) Quantity Sold Each Quarter 10 2,000 20 1,800 30 1,600 40 1,400 The cost to produce each item is £5.(a) Plot the data with quantity sold q on the y-axis and the
1. (a) Total capital required = £120, 000. To calculate the additional capital we are required to calculate the difference between the initial capital requirement and what is invested by your partner and venture capitalist, i.e.120, 000 − 30, 000 − 55, 000 = £35, 000(b) Percentage of the
4. Given the cost function C (x) is given by C (x) = 2√x −4x2 +2x, calculate the marginal costs when x = 40 and x = 120 giving your answers to two decimal places.
3. Given the cost function C (x) is given by C (x) = x3 + 2x2 + 340, calculate the marginal costs when x = 200 and x = 350.
2. You own a production factory that is capable of producing 60,000 widgets per day. The daily cost of producing w widgets is given by:C (w) = 240,000 + 0.08w + 200,000,000 wHow many widgets per day should you manufacture in order to minimise production costs and what would be the associated cost?
1. You own an apartment complex that has 300 apartments to rent out. If you rent out x apartments then your monthly profit in pounds is given by:P (x) = −8x2 + 3,200x − 72,000 How many apartments should you rent out in order to maximise profit and what would your maximum profit be?
Determine the position and nature of the stationary points of the following functions.1. y = 3x4 − 8x3 − 3 2. y = x4 + 32x 3. y = (x + 2)(x2 − 3x + 5)4. y = 12 √x − x32− 10 x > 0 5. y = 6 − 3x − 4 x3 x ≠ 0
3. Calculate the value of the gradient of y = e2x + 1 at the point (0, 2).
2. Calculate the value of the gradient of y = x3 + 2x2 + 1 at the point (2, 17).
1. Differentiate the following functions with respect to the variable given in brackets:(a) y = 2x3 + 4x2 + 2x − 1 (x) (b) y = e−2x + 2 (x)(c) y = ln(5t) + t3 + 2t2 − 1 (t) (d) y = −2 ln(t) − 3e2t − 4t (t)(e) y = x2 + 3x + 2 (x) (f ) y = ln(2x) + ex (x)(g) y = 3e4t + 2t2 (t) (h) y =
3. A hypothesis test was performed and the conclusion was that there was evidence to reject the null hypothesis. On further investigation you found that the null hypothesis was actually true and it should not have been rejected. Was an error made and if so what type?
2. You perform a hypothesis test with the null hypothesis being that the average graduate salary was £28,500, with the alternative hypothesis being that it was not £28,500. From the statistical test it was found that there was evidence to reject the stated null hypothesis.After further
1. You perform a hypothesis test with a null hypothesis that the average amount of money spent in the January sales was £1,200 against the alternative that it was greater than£1,200. After performing the hypothesis test you found that there was no evidence to reject the null hypothesis. After
4. You produce 20kg bags of sand. There have been customer complaints that the bags are undersized. You take a sample of 15 bags and find the following weights:19.5, 19.8, 20.2, 19.1, 18.9, 20.4, 20.1, 19.8, 19.5, 20.4, 20.5, 19.1, 19.5, 19.7, 19.6 Mean = 19.74; S.D. = 0.501. Can you be 95%
3. You release a new product of which 10% are returned due to a fault. You tweak the manufacturing process in a bid to improve quality. After the tweak you find that 8% of the next 100 items are returned faulty. Can you be 95% confident that you have improved the manufacturing process?
2. You currently sell on average 1,500 units per week. You started an initiative to encourage more sales. After the initiative you have recorded the following 10 weeks of sales:1550, 1601, 1604, 1480, 1498, 1501, 1620, 1540, 1490, 1502 Mean = 1538.6; S.D. = 52.84. Can you be 95% confident that
1. It has recently been reported that 50% of your customers report waiting for less than 5 minutes to speak to customer services in the call centre. You have recently hired more call staff in an attempt to speed up the process for the customers. Three months after hiring the new staff it was found
1. The number of visitors to a theme park during a randomly chosen time were recorded on eight different occasions and were found to be as follows:1382, 1478, 2002, 1784, 1564, 1841, 1753, 1801(a) Calculate the sample mean and sample standard deviation for the number of visitors.(b) Assuming the
3. You run a second hand car garage. The number of cars sold over the last six months is given in the table below:Month 1 2 3 4 5 6 Sales 12 8 18 14 21 14 Estimate the trend over the given six month period using(a) 3 point moving averages.(b) 5 point moving averages.(c) Centred 4 point moving
2. You are the manager of a mobile phone store. The number of phone contracts sold over the last twelve months is given in the table below:Month 1 2 3 4 5 6 7 8 9 10 11 12 Sales 126 378 218 194 231 194 195 181 201 143 150 175 Estimate the trend over the given twelve month period using(a) 5 point
1. You are the manager of a shop selling bathrooms. The number of bathrooms sold over the last eight months is given in the table below:Month 1 2 3 4 5 6 7 8 Sales 10 12 8 9 3 9 5 12 Estimate the trend over the given eight month period using(a) 3 point moving averages.(b) centered 4 point moving
3. A multiple regression analysis is run to look at the factors that effect a student’s exam performance. It is thought that attendance in lectures, hours revising and coursework mark are the main factors that effect the performance. Using the SPSS readout below:(a) Determine which of the factors
2. A multiple regression analysis is run to look at the factors that effect a person's salary. It is thought that years of experience, years in education and gender (male = 0 and female =1) are the main factors that effect the person’s salary. Using the following SPSS readout:(a) Determine which
1. A multiple regression analysis is run to look at the factors that effect the value of a house. It is thought that distance to the city centre (in miles), number of bedrooms and the size of the garden (m2) are the main factors that effect the value of a house. Using the following SPSS readout:(a)
3. You are investigating the relationship between customer waiting time and customer satisfaction. Calculate the line of best fit for this data.Waiting Time (minutes), x 15 10 8 9 18 6 Satisfaction (%), y 54 71 89 91 25 90 If someone had to wait 12 minutes, what would you expect their level of
2. A test is administered to all new employees at the end of their basic training. Calculate the line of best fit for this data.Training Test, x 67 43 87 93 21 35 45 Performance After One Year, y 63 75 21 69 72 71 89 If someone had a score of 58% what would you expect their performance score to be?
1. The table shows the number of visitors to the UK (in thousands) and the amount of money that they spent (millions). Calculate the equation of best fit for this data.Number of visitors (thousands), x 1,670 1,241 2,568 2,625 2,186 1,513 1,001 2,033 Amount of money spent (millions), y 112 131 168
1. The following table shows the number of visitors to the UK (in thousands) and the amount of money that they spent (millions). Calculate the Pearson’s correlation coefficient for this data.Number of visitors (thousands), x 1,670 1,241 2,568 2,625 2,186 1,513 1,001 2,033 Amount of money spent
2. Calculate the standard deviation for the following data sets.(a)Value Frequency 100 8 120 13 140 12 160 23 180 8(b)Value Frequency 10 7 11 12 12 9 13 3 14 12
1. Calculate the range, interquartile range and sample standard deviation for the following sets of data.(a) 100, 120, 89, 156, 200, 156, 186, 156, 176, 172, 193, 100, 101.(b) 12, 15, 17, 12, 13, 14, 10, 12, 5, 8, 12(c) 54, 55, 50, 48, 38, 38, 30, 38, 54, 32, 19, 20, 21
2. Constance introduces a new drink to her cafe menu. She wants to sample 20 of her customers about the new drink. The table below shows how many customers ordered the new drink during the last week based on age and gender.16 - 25 26 - 35 36-45 46-55 56 or older Female 14 2 20 28 5 Male 18 5 15 11
1. You wish to investigate the thoughts and opinions of the staff that work in your department.The following descriptions of different sampling methods are given below, which method are they?(a) You approach the first 20 members of staff that enter the building in the morning.(b) Members of staff
1. Consider the following line chart showing how the inflation rate has changed in the UK since 1984.(a) What was the highest rate of inflation since 1984 and in which year did it occur?(b) What was the lowest rate of inflation before 2015 and in which year did it occur?(c) What is the difference
2. You own an ice cream store and you are looking to expand your business. The payoff table shows the profit associated with expanding your current store or opening a new store based on three states of the economy (figures are profit, in thousands of pounds).Growing Economy Stagnant Economy
1. The following payoff table shows the profit associated with a decision analysis problem with two decision alternatives and three states of nature.State 1 State 2 State 3 Decision 1 150 280 240 Decision 2 240 230 220(a) If you know nothing about the probabilities of each of the three states
6. Assuming a random variable x follows a normal distribution with mean μ = 12 and σ = 3 re-write the following probabilities in terms of their z-score(a) P(x < 15)(b) P(x > 9)(c) P(x > 14)
5. There are on average 10 visitors to a hospital per hour. Assuming the number of visitors follow a Poisson distribution calculate the following:(a) The probability that there are fewer than 2 visitors in an hour.(b) The probability that there are more than 12 visitors in an hour.(c) The
4. There are on average 12 phone calls per hour to a call centre. Assuming the number of phone calls follow a Poisson distribution calculate the following:(a) The probability that there are fewer than 10 phone calls in an hour.(b) The probability that there are more than 15 phone calls in an
3. You own a factory that produces components of which 2% are known to be defective.The components are packed into boxes of 20. A box is selected at random.(a) Find the probability that the box contains exactly three defective components.(b) Find the probability that there are at least two
2. The probability of a telesales representative making a sale on a particular customer call is 0.2. Calculate the following:(a) The probability that there are exactly 5 sales in 10 calls.(b) The probability that there are more than 4 sales out of 10 calls.
1. In your restaurant you have found that 2 out of every 5 customers ask for a glass of water with their meal. A random sample of 12 customers is selected.(a) Calculate the probability that exactly 7 customers ask for a glass of water with their meal.(b) Calculate the probability that fewer than 9
6. You have developed a screening methods for a virus that causes a serious illness which is believed to occur in 1 in every 500 people. The screening method indicates correctly when the person actually has the illness. From testing it has been shown that a false positive occurs 2% of the time.
5. You manufacture two products, product A and product B, in equal proportions. It has been found that 12% of product A and 14% of product B are faulty. Calculate the probability that if a product was faulty it was product B.
4. From your market research you find that 89% of students own a smart phone and 65%of students own a tablet and a smart phone. What is the probability that a student owns a tablet given that they own a smart phone.
3. The probability that it is Friday and a member of staff is off sick is 0.13. Assuming that there are only five working days in the week, calculate the probability that a member of staff is sick given that it is Friday.
2. Your lecturer sets two exams. 30% of the class passed both exams and 45% of the class passed the first exam. What percentage of those students who passed the first test also passed the second test.
1. The following data on the sports that students play are summarised below:Football Water Polo Fencing Badmington Swimming Total Female 40 25 55 45 55 220 Male 72 45 12 54 27 210 430(a) Calculate the probability that a student plays waterpolo given they are female.(b) Calculate the probability
5. You have two machines, A and B, in your factory. The probability, at any given time of them working or have failed is below:Machine A working Machine A not working Machine B working 0.80 0.05 Machine B not working 0.13 0.02(a) What is the probability that both of the machines have failed at any
4. An unfair die is rolled 250 times and the following results were obtained.Outcome Frequency 1 15 2 24 3 40 4 95 5 56 6 20 Calculate the probability of rolling a 6.
3. If you roll a die three times, what is the probability of rolling three odd numbers in a row?
2. You toss a coin and roll a fair dice. Calculate the probability of tossing a tail and rolling a 4.
1. Write down the sample space of tossing a coin and rolling a dice.
3. Solve the following equations using the method of completing the square.(a) x2 + 4x – 3 = 0(b) –x2 + 2x + 4 = 0(c) 3x2 + 9x – 2 = 0
2. Solve the following equations using the quadratic formula.(a) 2x2 – 3x –12 = 0(b) –2x2 –5x + 2 = 0(c) 2x2 –5 = 0
1. Solve the following equations using the method of factorisation.(a) x2 + 4x = –3(b) x2 + x = 2x + 2(c) 2x2 – 3x = 2
2. You are manufacturing two types of toy, toy A and B. The toys are sold at £25 and £20 respectively. You have 2,000 units of resource available in total, with toy A requiring 20 units to manufacture whilst toy B requires 12 units. It takes 5 minutes to manufacture each toy. Your factory is open
1. You have recently acquired 110 hectares of land. You have decided to grow wheat and barley on the land. Due to the region’s excellent climate, the entire production of wheat and barley can be sold. You want to know how much of each variety you should plant, given the costs, net profits and
Solve the following pairs of simultaneous equations:1. 2x + 3y = – 4 and 3x – 4y = 11 2. x – 3y = –2 and –2x + 3y = –2 3. 6x + y = 1 and 2x – 3y = 7 4. –3x – 3y = 6 and 3x + 2y = –1 5. –3x + 2y = –2 and – 4x + y = – 6 6. 12x – 13 y = 0 and x + 2y = 6 7. 2x – 7y = 24

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Business Analytics In Context : An Introduction To Methodologies 1st Edition Gareth Woods - Solutions

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