Question 1

(a)  Normalization will play an important role in analysing the CO2 emissions data. In Exhibit 1 we

include some data for China for the years 1990 and 2016.

Exhibit 1

(i)          Write the formula used to calculate GDP per capita for 2016 and outline the units of measurement of this variable. [2 marks]

(ii)          In Exhibit 1, I have also calculated the percentage change in GDP, GDP per capita and

CO2 emissions between 1990 and 2016. Write the formula showing how to calculate the percentage change in CO2 from 1990 to 2016. [1 mark]

(iii)         Briefly discuss overall trends in the percentage change in GDP, GDP per capita and

CO2 emissions between 1990 and 2016 and their relationship to other variables. [3 marks]

(b)  The main focus around CO2 emissions is reducing them in order to control climate change. Let

us investigate which sorts of countries have been able to reduce CO2 emissions per capita between 1990 and 2016.

I have constructed two categorical variables:

• Decreased CO2 per capita:

•    Yes = the country reduced per capita CO2 between 1990 and 2016,

•    No = the emissions per capita rose over this period.

• Income Level:

•    Low Income = GDP per capita<$5,000 in 2016,

•    Middle Income = GDP per capita from $5,000 to $15,000 in 2016,

•    High Income = GDP per capita>$15,000 in 2016.

Exhibit 2 reports a pivot table of counts of countries in each cell.

Exhibit 2

(i)          What does the value 29 represent in Exhibit 2? [2 marks]

(ii)          How many countries’ data are used to construct Exhibit 2? [1 mark]

(iii)        What  is the  probability that a  randomly  selected  country  is  Middle  Income  and  had

decreased CO2 emissions per capita over the period 1990 to 2016? [1 mark]

(iv)         Using the numbers in Exhibit 2, write the formula to calculate the following probabilities:

P( Decreased CO2 per capita = Yes | Income Level = High Income )    P( Decreased CO2 per capita = Yes | Income Level = Middle Income ) P( Decreased CO2 per capita = Yes | Income Level = Low Income )     P( Decreased CO2 per capita = Yes ) [4 marks]

(v)          Using the probabilities you calculated in the previous question, discuss whether you think that a country’s income level is independent of whether their emissions per capita fell between 1990 and 2016. [2 marks]

(vi)        What do the probabilities you previously calculated tell you about which sorts of countries

have been successful in reducing their CO2 emissions per capita. Provide evidence for your answer. [2 marks]

(c)   Let us examine the different sources of CO2 emissions across time. In Exhibit 3 we report data for the World over the years 1800, 1900 and 2000.

Exhibit 3

(i)          The sources of CO2 emissions in the year 1800 are different from the others, how and why? [2 marks]

(ii)          Using Exhibit 3, calculate the change in CO2 emissions from gas between 1900 and 2000. [1 mark]

(iii)         Using Exhibit 3, calculate the percentage share of CO2 emissions from oil in 2000. [1 mark]

(iv)         Using Exhibit 3, calculate the percentage change in CO2 emissions from coal between

1900 and 2000. [1 mark]

(v)         Which of the sources of CO2 emissions has been the major contributor to the increase in emissions from 1900 to 2000. Provide evidence for your argument. [2 marks]

(vi)         Focusing on the data for the year 2000 in Exhibit 3. What sort of graph would be best-

suited to present this information and why? [2 marks]

Question 2

(a)  Exhibit 4 provides some descriptive statistics for CO2 per capita and GDP per capita in 2016.

Exhibit 4

(i)           Focusing on the mean and the median, discuss the skewness of these two variables. [2 marks]

(ii)         The mode is another measure of central tendency. Define the mode. With reference to

the modes in Exhibit 4, discuss how useful the mode is as a measure of central tendency for the two variables. [3 marks]

(iii)        Outline in words how the range and the sample standard deviation are calculated. Discuss

which you think is the best measure of the spread of a distribution. [3 marks]