# Quantitative Analysis Essay Sample

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Question 1 – 5 Points
Leila took a standardized test and was told that her score was in the 89th percentile. Explain clearly and in only one sentence what this means. Notes:

 Percentiles are a way of describing the position of a particular score within a set of scores  As per the question, I was looking for one simple sentence to explain the meaning of the statement Ideal Answer: If Leila’s score was in the 89 percentile this means that Leila scored higher than 89% of participants in the test. th

Question 2 – 10 Points
A gas station near the Emirates Road is revaluating its gasoline-fuel reorder point. The gasoline fuel level in its main tank triggers an automatic replenishment order. The daily demand faced by the station for gasoline is normally distributed with an average of 8,000 liters and standard deviation of 2,500 liters. After the automatic order is placed, the gasoline-fuel is received at the gas station in exactly 3 days. In other words, it takes three days lead time for the gasoline to be replenished after the order has been made. At what volume should the re-order point be set to ensure that the station’s chance of being out of stock during the replenishment period is limited to a probability of 5%? Notes:

 Those people who did not score full points on this question usually made it more complicated than it is.  This question is very similar to many exercises we did together in class. The only complication is the three days of lead time – which was added to make the question more realistic for an actual business situation. Ideal Answer: µ = 8000; S = 2,500; Alpha = 0.05

 The average consumption is 8000l, with a standard deviation of 2,500l.  In order to identify the range of daily usage that has a 95% probability of occurring, we need to look at the range +/- two standard deviations = 3,000l to 13,000l

 In order to ensure we don’t go out of stock we need to take into account the maximum likely usage of fuel per day that includes 95% of possible outcomes = 13,000l (not 3000l)

 In order to make sure we don’t go out of stock for 3 days we need to assume that the maximum amount of fuel is used for 3 days = 3 x 13,000 = 39,000l

 Therefore, in order to ensure that we have only a 5% chance of going out of stock when it takes 3 days for the fuel to arrive, we need an automatic replenishment order to be placed when the level in the fuel tank reaches 39,000 litres. (Note: Some of you submitted the answer 36,300l based on calculating a one-tailed range. This answer also scored full marks, although I did not expect anyone to do this because we did not have the time to cover one-tailed ranges on the course).

Dr. Amanda Nimon Peters Nov 2012

Question 3 – 20 points – you may not exceed this page
Notes:

 The key to this question was the ability to pull useful observations from the data, and write those observations in a manner that would have clear meaning for senior management.

 There are many different perspectives that you could take on the data. The most useful would be to draw conclusions for the country/region in which you work, or the country/region that is most important for your business. Ideal Answer: These are just some examples of strong answers. There are many that are possible. Conclusions

The survey found that on average across the Middle East, employees feel engaged and motivated in their current jobs (80% agreed they felt engaged; 74% agreed they felt motivated to perform well). In contrast, Middle Eastern workers appear to be less happy about the conditions of their employment. This is reflected in the lower levels of agreement to ‘feeling that the organisation deserves their loyalty’ (60%). Further, while they said they would speak highly of their organisations’ products and services (74%); there was a noticeable drop in the number who would speak highly of their organisation as an employer (66%). Further, most employees are not planning a long term commitment to their companies. Across 10 of 11 countries surveyed, less than half of all respondents expect to be in the same company in one year’s time.

This figures drops to 24% for those who expect to be in the same company in three years’ time. The trends in the UAE are in-line with regional trends, except that UAE workers are slightly below the average on feeling loyal to the organisation. It is important to note that the sample of employees used in this survey may not accurately reflect the attitude of the working population as a whole. The study was conducted by Bayt.com, an on-line job search company. Although the study methodology was not published, it is likely that the sample was drawn from visitors to the website – who are by definition more likely to be looking for a new job and therefore less satisfied with their current employer.

Recommendations

Businesses in the Middle East should consider widening their recruitment criteria to positively select for people willing to commit for a minimum of three years. If it is true that the average employee expects to change his or her employer in as little as a year, it will be difficult to obtain a return on investment from employees. There may be an opportunity for companies to increase employee satisfaction and retention through devising and communicating better career path planning. If employees can see there is a career plan for them, they are more likely to imagine themselves staying in the same organisation for the coming few years. Dr. Amanda Nimon Peters Nov 2012

Question 4 – 10 points – you may not exceed this page
In a 2005 study, The Economist linked objective measures of specific conditions within a country to the average life-satisfaction score of citizens surveyed in that country. The average life-satisfaction score is calculated from a series of questions such as “On the whole are you very satisfied, fairly satisfied, not very satisfied, or not at all satisfied with the life you lead?” The paper published by The Economist provides sufficient justification of the way it calculates average Life Satisfaction within a country. We can also assume that the sample size and sampling method are appropriate. The Economist’s researchers identified nine objective measures which together predict the average life-satisfaction rating within a country with a correlation coefficient of 0.92, a pretty accurate model.

Coefficient Constant 2.7959 GPD per person 0.0003 Life expectancy 0.0448 Political freedom -0.1052 Job security -0.0217 Family life -0.1878 Climate and geography -1.3534 Political stability 0.1519 Gender equality 0.7423 Community life 0.3865

Unit of measure. Source USD. Source: Economist Intelligence Unit Years. Source: US Census Bureau completely free =1 to unfree = 7. Source: Freedom House Unemployment rate %; Source: Economist Intelligence Unit; ILO Divorce rate converted into a score of 1 (lowest divorce rates) to 5 (highest); Source: UN / EU-romonitor Latitude, to distinguish between warmer and colder climes. Source: CIA World Factbook Political stability and security ratings as defined by The Economist Ratio of average male and female earnings. Source: UNDP Human Development Report Dummy variable: 1 if country has high rate of church attendance or trade-union membership, 0 otherwise. Source: ILO

Answer the following questions in simple sentences, not exceeding the space provided. Which variables would you expect to have negative effects on life satisfaction? Is this supported by the results or are there relationships reported that seem counterintuitive? If yes, which one(s)? Ideal Answers: It seems counter-intuitive that political freedom, job security and family life would have a negative linear relationship with life satisfaction scores. However, these negative relationships are simply the result of the scale that has been used. The study shows in fact that life satisfaction goes up as political freedom increases, unemployment decreases, and divorce rates decrease, i.e. in line with expectations. It is interesting that life satisfaction increases as latitude decreases, meaning that people are happier when the climate is warmer. This suggests that life satisfaction would be even higher in northern European and North American communities if they were closer to the equator, all other factors remaining constant.

The most surprising relationship reported is that between life satisfaction and gender equality. According to the table above, satisfaction increases as the ratio of male to female wages increases. Given that decades of wide-scale research has shown that quality of life within a country increases as gender equality increases, we must assume that the scale is incorrectly expressed: I believe they meant that life satisfaction increases as the ratio of female to male earnings increases. The study mentions other predictors that were not included because they provided no further predictive power to their model.

Does this mean that education is not related to quality of life? Explain what must have happened when they added the variable “education.” Ideal Answer: The model created by this research has identified nine factors that independently increase the predictive power of their model. There will be many other factors that are correlated with life satisfaction that are already taken into account in the model via other variables. For example, ‘education’ may already be accounted for in life expectancy, political freedom and 2 gender equality. When education was added to the model, adjusted R did not increase, indicating that this variable made no independent contribution. Dr. Amanda Nimon Peters Nov 2012

Question 5 – 10 points – you may not exceed this page
Study the charts at the bottom of the page (Figures b & c). Assume that the data was collected in a valid manner, with a sufficiently large sample size. Express clearly and simply the major conclusion from Figure b The data indicate that there is very little relationship between per capita healthcare expenditure and an increase in life expectancy for men over the age of 67 years. Expenditure of up to \$1500 per person cannot be expected to increase life expectancy in this age group beyond a few additional months. Is there anything else you want to add about this conclusion? This is a surprising finding. As there is widespread evidence that per capita healthcare expenditure improves life expectancy at a population level, this data suggests that the investment might be more important when men are younger. It may be that expenditure on younger men helps to determine their long-term health and life expectancy.

Perhaps expenditure on men’s’ health once they are in this age group is ineffective. Express clearly and simply the major conclusion from Figure c The data indicate that there is a strong negative relationship between solar radiation and overall cancer rates. This means that increased solar radiation is related to a lower incidence of cancer as an overall disease. Is there anything else you want to add about this conclusion? This is also a surprising finding as it is also known that high levels of solar radiation can actually cause certain types of skin cancers. A correlation does not indicate that one variable causes the other, so this figure does not show that increased sun exposure will cause lower rates of cancer, but it does suggest that the relationship between cancer and solar radiation is more complex than we may have believed. Based on the above statements, what, if any recommendations would you make to the Minister of Health?

1. It is worth investigating the differential impact of healthcare expenditure on life expectancy amongst different age groups. It may be that health care investment brings greater population benefits when made amongst young adults or middle-aged people. Further, it seems that solar radiation levels up to a value of around 520 units may be beneficial to a population. It would be worthwhile at least commissioning a study to establish the average solar radiation exposure in your population before taking further steps.

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