What is sampling and what are its uses

Quantitative Methods

What is sampling and what are its uses

Case Studies
Multi Criteria Decision Making (20 Marks)
MCDA. (multi criteria decision analysis) is considered to be one of the fastest growing research operations in the last several years. The researcher focus towards MCDA led to development of many different approaches and ways in the field. There are two types of
procedures: theoretical assumptions and decision addressed type. This difference throws challenges to the procedure of choosing the most ideal method for the decision making problem. Most of the time, the initial approach towards applying MCDA in the real world problems relates to the set up of simple understanding Of the context and recognizing the problem of decision. This step includes the ones• who make decisions and other important participants who make important contributions for the MCDA procedure by sharing their knowledge. The common insight of the decision framework is received by knowing the goals of the decision making body and recognizing not only those people who make decisions but also those who face the decision. • Dooley (2009) says that the first three steps take up more time in the process of MCDA, particularly because of their qualitative features. Assigning of comparative significant weights to the selected criteria is the next step: These weights can be ascertained directly, for example ranking, swing, trade off; or indirectly, for example- centrality, regression and interactive. Later, the DM has to give individual scores, considering his or her views, to each of the recognized options according to the criteria which seem vital. These scores show the decision of DM . related to spreading of each substitute to every performance standard. The information which is attained is maintained distinctively into performance template, which is also as consequence matrix, options matrix, or just decision table. The next process includes abstract of the information consisting of the performance matrix in the form of multi criteria scores, for every possible plan. Mostly,
this is attained by combining the individual scores of matrix so that total valuation of .each substitute which allows more comparison. The groups of substitute ranked on the basis of all these scores. Finally, the procedure can include a warm evaluation of the outcome to amendments in the scores or criteria, to conclude the sturdiness of the result of MCDA. At the end, the analysis and tradeoffs included in the respective choices are given to and conferred with the DM. In many cases, the ultimate decision that DM takes, does not match with the highest level of alternative, as they are more focused towards the process of knowing the effect of each and every factor in ranking of choices than in the exactness of the ranking. Also, it should be observed that the generalizations are not used to of the outcome given by the process of MCDA, and they only appropriate for the group of choices which were assessed.
Answer the following question.
Q1.What role does MCDA play in decision making? (Hint: MCDA is considered to be one of the fastest growing research operations, these scores show the decision of DM related to spreading of each substitute to every performance standard)
Q2. What does MCDA stand for? (Hint: multi criteria decision analysis)
 

What is a simple linear regression model

CASE STUDY (20 Marks)
The cost of fuel in running of an engine is proportional to the square of the speed and is Rs 48 per hour for speed of 16 kilometers per hour. Other expenses amount to Rs 300 per hour. What is the most economical speed?
Answer the following question.
Q1. What is most economical speed?
Q2. What is a chi-square test?
Q3. What is sampling and what are its uses.
Q4. Is there any alternative formula to find the value of Chi-square?
A Network Rail (20 Marks)
The railways play an important role in the economy and infrastructure of Britain. Not very many people travelled back jn the 1920 as compared to present time, in spite of 50% reduction in raif routes as compared to the 1960s. Rail is also used for transporting goods around Britain. Rail proves to be• more eco-friendly and safest means of transportation as compared to other vehicles so, not surprisingly, the number of people commuting have gone 40% more since the past ten years. By 2034, this figure can go up. The work of network rail has to look after the tracks, bridges and tunnels which comprises of the British rail network. The railway infrastructure is made up of signals and level crossings. It has to look after the 20,000 mile long track and 40,000 bridges and tunnels. Britain’s 18 main rail stations, from Edinburg Waverley to London King’s Cross, are looked after by the Britain rail system. Ten years ago, when the network rail took up these responsibilities, • it had to face some challenges. The rail neork was facing some problems. Trains were running late, the costs were too high and there was shortage of assets in both the people and machinery. Due to these issues, people had less confidence in the rail network. Ever since then, rail network has aimed at sustaining operations to reduce the expenses. There has been 28% reduction in expenses mainly because of economy of scale. New tracks and machinery have been bought, and there has been 90% rise in the rail punctuality. Huge projects have been given on time an towards the budget, as a result the confidence of the people has improved. Rail network has moved from ‘find and fix’ to ‘predict and prevent’ policy. This has proved to be more cost effective and competent and enabled in avoiding delay or obstruction for the people in their travel. The rail network invested approx. 12 billion pounds between 2009 and 2014, towards the rail network. Britain has the fastest developing network in whole of Europe. By investing in people, the rail network is investing in the future to. .Britain has the largest working personnel of 35,000 workers. It has people working in various positions, like, engineers for maintenance and signaling to project managers. Each area offers an opportunity to work. They also consist oil HR (human resources), IT (information technology), and finance and customer service. Network Rail needs to employ and keep capable engineers in order to get the work done. Presently, its engineers are doing some oi the most stimulating projects in Europe. The projects include HS2, which is the new super spited rail link between the north and south Britain, and the project of London Crossrail. Some oi the biggest and busiest rail stations are being upgraded, like, London King’s Cross and Birmingham New Street. The main focus of the HR of Network Rail is to recruit various personnel. This not only deepens the culture of business but it also makes sure that it can reach every talent. It offers training for every applicant, whether he is a school drop-out or a graduate, whether male or female, a continued flow of appropriate talent is ensured to keep its long term project going. The company about gives many opportunities to its workers to receive recognized qualifications, such as an exclusive programme in post graduation, sponsoring the Master’s Degree in project management and trainee.
Answer the following question.
Q1.What were the initial problems that Network Rail of Britain face? (Hint: It has to look after the 20,000 mile long track and 40,000 bridges and tunnels. Trains were running late, the costs were too high and there was shortage of assets in both the people and machinery)
Q2. What is the new super speed rail link between the north and south Britain called? (Hint: HS2)
CASE STUDY (20 Marks)
The price P per unit at which a company can sell all that it produces is given by the function P(x) = 300 — 4x. The cost function is c(x) = 500 + 28x where x is the number of units produced. Find x so that the profit is maximum.
Answer the following question.
Q1. Find the value of x.
Q2. In using regression analysis for making predictions what are the assumptions involved.
Q3. What is a simple linear regression model?
Q4. What is a scatter diagram method?

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