New Canadian Motor Vehicles Co2 Emissions Samples for Students

Question: Write a Report on New Canadian Motor Vehicles Co2 Emissions. Answer: This report is in response to your memorandum dated 4th January 2017. You have requested me to conduct an analysis of the recent automobile CO2 emissions as provided in the data file attached to your memorandum. There are some specific questions that you would like answered based on the data provided. Overall Summary of CO2 Emissions On analyzing CO2 emissions, Fiat recorded the lowest CO2 emission at 186.46 g/km while Aston Martin recorded the highest CO2 emission at 347 g/km. On further analysis the overall average CO2 emissions based on the 1,082 observations was 244.69 g/km associated with a standard deviation from the average of 55.70 g/km. In addition, analysis suggested approximately normal distribution based on a slight positive skew-recorded at 0.63 and this is evident when looking at the histogram on the CO2 emissions. You can be 95% confident that the average CO2 emissions will be 244.69 g/km 1.69 standard errors. That is to say, you can expect the average CO2 emission to fall between 243 g/km and 246.38 g/km based on a sample of 1,082 observations. Relationships with CO2 Emissions You were interested to know whether there was any relationship the CO2 emissions and the type of fuel used. According to the data, there were four types of fuel namely; regular petrol, premium petrol, diesel and ethanol. In essence your question was; is there any difference between the observed proportions of the fuel used and the expected proportion? To determine this, a chi-square test, which is a non-parametric test, was carried out. According to Kingoriah (2004), a chi-square test is used to investigate whether there is a difference between the observed proportion or frequency distribution among categories and the expected frequency distribution. Under the null hypothesis, there should be no difference between the expected and observed distribution of fuel types. Based on your question the hypothesis is; H0: There was no statistically significant difference between CO2 emissions and the type of fuel used (null hypothesis) HA: There was some statistically significant difference between CO2 emissions and the type of fuel used (alternative hypothesis) According to the analysis, there seemed to be some notable differences between the observed CO2 emissions and the expected CO2 emissions. The observed CO2 emissions for regular petrol was recorded at 233.22 g/km, premium petrol was 256.10 g/km, diesel was 220.46g/km and ethanol was 268.03g/km. The expected average CO2 emission was 245.46g/km. The question therefore was to determine whether these differences were statistically significant to make an inference of the entire population? The results revealed a p value of 0.13. This was greater than the cut-off point of 0.05 (alpha level). The decision was to fail to reject the null hypothesis and conclude that there is no evidence based on the sample data to suggest that there are differences in CO2 emissions based on the fuel used. The differences observed in our sample data could have resulted from sampling error of chance. Confidence Intervals On Estimation of the Level of CO2 Emissions for 4 Cylinder, 6 Cylinder and 8 Cylinder vehicles Your other concern was to estimate the level of CO2 emissions for all 4 Cylinder, 6 Cylinder and 8 Cylinder vehicles and whether there appears to be any difference. At 95% confidence level you can expect the mean level of CO2 emissions for a 4 cylinder motor vehicle to be between 198.38g/km and 203.46g/km. Likewise, at 95% confidence level we can expect the mean level of CO2 emissions for a 6 cylinder motor vehicle to fall between 255.39g/km and 260.97g/km. For the 8 cylinder motor vehicle we can be 95% confident that the mean level of CO2 emission will fall between 277.08g/km and 284.48g/km. Estimation of the Proportion of All Vehicles That Have 4 Cylinders, 6 Cylinders And 8 Cylinders You were also concerned on the approximate proportion of all vehicles that have four Cylinders, six Cylinders, and eight Cylinders. The proportion of four cylinder motor vehicles was 45.19 per cent of the total observations of 1,082. We can expect that at 95% confidence level that the proportion of four cylinder motor vehicles will fall between 42.23% and 48.16% of the true population proportion. Likewise, the six-cylinder motor vehicles proportion was 35.49 per cent with an expected proportion of the entire population of between 32.64% and 38.34 per cent. The eight cylinder motor vehicles had a sample proportion of 19.32 per cent hence we can be ninety-five per cent confident that the true proportion of eight cylinder motor vehicles will be within 16.96 per cent and 21.67 per cent. Hypothesis Tests A month prior to your memo, a national newspaper published an article indicating that the Federal government was investigating a proposal to limit CO2 emissions for new motor vehicles to a maximum of 350 grams per kilometre. The same article proposed that this was likely to eradicate a minimum of five per cent of the biggest polluting motor vehicles off the roads. You are concerned whether the sample data is able to support this claims. For the limit of CO2 emissions of new motor vehicles to a maximum of 350 grams per kilometre, your concern was to determine whether there was evidence from the sample data to support the claim that new vehicles were emitting no more than 350g/km of CO2 at 5% level of significance. The hypothesis formulated hence was; H0: CO2 emissions for new motor vehicles was more than 350 grams per kilometre (null hypothesis) HA : CO2 emissions for new motor vehicles no more than 350 grams per kilometre (alternative hypothesis) The decision was to reject the null hypothesis and conclude that CO2 emissions for new vehicles was likely to be more than 350g/km (t= - 62.20, p .01). Accordingly, the article also suggested that the removal of vehicles emitting more than 350g/km of CO2 would eliminate up to 3% of the largest polluting vehicles off the road. However, was this true based on the sample data? The results did not seem to show any evidence that removing motor vehicles emitting more than 350g/km of CO2 would eliminate up to 3% of the highest pollutants off the road (z= - 6.71, p .01). Simple Regression According to your memorandum, you do not have much information about CO2 emissions. However, you reckon that the larger a vehicle engine is, the greater the CO2 emissions. You wanted to establish by use of a simple regression the degree of variation of CO2 emissions can be explained by the engine size of a motor vehicle. The simple regression analysis was carried out by taking engine size variable as the independent variable (denoted by x) and CO2 emissions as the dependent variable (denoted by y). As you correctly noted, the relationship between two or more independent variables and one dependent variable is best illustrated using a regression model. In this case, your concern is how much CO2 emissions are likely to predicted by the engine size of a motor vehicle. According to Lucey (1996), a regression model amalgamates one or various independent variables to determine one single dependent variable. The regression model was therefore formulated as: Y = a + X Where Y = CO2 emissions a = intercept = engine size The coefficient of determination represented by R square in the analysis seeks to investigate the degree of variation of the dependent variable (in our case it is CO2 emissions) that can be explained by the independent variable or predictor which in our case is engine size. According to my investigation, 0.7014 or 70.14% variability of CO2 emissions can be explained by a change in engine size. This means that thirty per cent of a change in CO2 emissions is explained by other factors other than engine size. The next step sought to determine whether there existed any statistically significant linear correlation between engine size and CO2 emissions. In short, whether there was any statistically significant correlation between engine size and CO2 emissions. The hypothesis was stated as follows; H0 : = 0:There is no statistically significant difference in change in engine size and CO2 emissions. HA : 0:There is some statistically significant difference in change in engine size and CO2 emissions. The analysis of variances table revealed an f-statistic of 2540.20 associated with a p value of p 0.01. The decision was therefore to reject the null hypothesis and conclude that there was evidence to suggest that a change in engine size is likely to affect CO2 emissions (f= 2540.20, df= 1,p .01). However, it should be noted that this is only a causal relationship. That means that a relationship between engine size and CO2 emissions does not automatically infer that the tendency of change in one variable is caused by change in the other variable. The regression model was statistically significant (t= 50.40, p .01). This meant that engine size was a good estimator of CO2 emissions. The regression model can be derived from the coefficients column as; CO2 emissions (y) = 130.32 + 30.59 (engine size). Using the model above it is possible to predict the CO2 emissions of a vehicle having an engine size of 1000cc or 1 litre. This can be done by substituting the engine size you would like to investigate as follows; CO2 emissions = 130.32 + 30.59 (1) = 160.91 X 1 = 160.91g/km Perusing through the data, I would have some concerns with the above prediction as there seems to be variations in CO2 emissions. For instance, an engine size of 1.50 litres has CO2 emissions of 140g/km while another vehicle of 1.40 litres has CO2 emissions of 173g/km. Inasmuch as the regression model may be used as a basis of predicting CO2 emissions using engine size as a predictor, other variables should be considered for inclusion in the regression equation. Appropriate Sample Size You were concerned that the sample size of 1,082 cars is far too many and we could easily achieve the same results with a much smaller sample size. In this regard, you would like to know whether similar results would be achieved with a smaller sample. For instance, if we wanted to estimate the proportion of vehicles whose CO2 emissions were less than 350 g/km to within 3%v margin of error, we would need to use data from the current study to make the estimation. This would include the estimated proportion of vehicles emitting less than 350g/ of CO2. From the sample, 1,040 cars have CO2 emissions less than 350g/km out of 1,082 cars sampled. This works out to 96% of the total sampled cars. From the analysis, the required sample size would be 164 cars (n=164). You also wanted to estimate the overall combined fuel consumption to within 0.5 margins of error of the mean at 95% confidence level. The sample standard deviation (2.90) was used to estimate the sample size. We would require a sample size of 135 cars to estimate fuel consumption. References King'oriah, G. K. (2004) Fundamentals of applied statistics. Nairobi: The Jomo Kenyatta Foundation. Lucey, T. (1996) Quantitative techniques. 5th edn. London: DP Publications (Low-Priced Edition).