ETF1100 Business Statistics Semester One 2021
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Semester One 2021
Exam - Alternative Assessment Task
ETF1100
Business Statistics
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
|
Country |
Year |
CO2 (millions of tonnes) |
Population (billions) |
GDP ($ trillions) |
GDP per capita |
GDP (% change) |
GDP per capita (% change) |
CO2 (% change) |
|
China |
1990 |
2,421 |
1.18 |
2.79 |
2,364 |
|
|
|
|
China |
2016 |
9,553 |
1.19 |
16.90 |
14,202 |
506 |
501 |
295 |
(i) Write the formula used to calculate GDP per capita for 2016 and outline the units of measurement of this variable.
|
GDP per capita in 2016 = 16.90 / 1.19 * 1000 = 14,202 Units of measurement: dollars per person. |
(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.
|
Percentage change in CO2 from 1990 to 2016 = ( 9,553/2,421 – 1 )*100 = 295% (Note: the formula alone is fine for full marks) |
(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.
|
GDP has grown by 506% over this period of 26 years. This is a very high rate (roughly 506/26=20% per year). GDP per capita has grown at 501%. This is only very slightly less than GDP, as population in China has remained fairly stable over this period. CO2 emissions have risen by 295%. This is roughly 10% per year . This is quite high but is lower than the growth of GDP. |
(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?
|
It is the number of countries which were High Income and did not have a fall in CO2 emissions per capita between 1990 and 2016. |
(ii) How many countries’ data are used to construct Exhibit 2?
|
160 |
(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?
|
16/160 = 0.1 or 10% (Note: Only the formula is required for full marks) |
(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 )
|
P( Decreased CO2 per capita = Yes | Income Level = High Income ) = 36/65 = 0.55 P( Decreased CO2 per capita = Yes | Income Level = Middle Income ) = 16/51 = 0.31 P( Decreased CO2 per capita = Yes | Income Level = Low Income ) = 11/44 = 0.25 P( Decreased CO2 per capita = Yes ) = 63/160 = 0.39 (Note: the final decimal value is not required for full 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.
|
No not independent. If these two events were independent then we would expect that all the probabilities we previously calculated would be equal. The fact that they are not indicates that a country’s income level does influence whether CO2 emissions per capita fell or not. |
(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.
|
The probabilities indicate that richer countries are doing better at reducing emissions per capita. There is a clear decline in the probabilities from High to Middle to Low income countries. |
(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
|
Year |
Cement |
Coal |
Flaring |
Gas |
Oil |
Other |
Total |
|
1800 |
0.000 |
28.092 |
0.000 |
0.000 |
0.000 |
0.000 |
28.092 |
|
1900 |
1.386 |
1873.155 |
0.000 |
11.542 |
67.532 |
0.000 |
1953.615 |
|
2000 |
715.796 |
8999.104 |
264.501 |
4745.742 |
10280.736 |
113.164 |
25119.043 |
2022-08-10