Part I: Each year the EPA does an analysis on the current models of vehicles sold in the United States. The data provided in the data set EpaFE2016Data.csv is a subset of this analysis for 2016 models. If you are curious you may access the full data set from the EPA website https://www.fueleconomy.gov/feg/download.shtml.
Two variables among this data set are fuel type and whether or not the car is made from an American car company or an International car company.
The fuel types are:
DU = Diesel, ultra low sulfur (15 ppm, maximum)
G = Gasoline (Regular Unleaded Recommended)
GP = Gasoline (Premium Unleaded Recommended)
GPR = Gasoline (Premium Unleaded Required)
a. Use the R code and instructions under Data Analysis 4 link in Canvas to create a table of counts among the two categorical variables and a stacked bar chart of the conditional proportion of fuel type among American and International car companies. Include your results. Briefly describe the plot and table.
b. What proportion of American car company vehicles require premium unleaded gasoline (GPR)?
c. What proportion of International car company vehicles require premium unleaded gasoline (GPR)?
Is there evidence the proportion of 2016 vehicles that require premium gasoline is different among the vehicles made by American and International car companies? Use a significance level of 0.01
d. State the null and alternative hypothesis to answer the question of interest.
e. Check Conditions. If they are not met state so and why. Proceed either way.
f. Calculate the test statistic.Show work by hand or if completed in R copy and paste code.
g. Obtain a p-value based on your calculated test statistic.
h. Calculate the 99% Confidence Interval. Show work by hand or if completed in R copy and paste code.
i. Give a four part conclusion (shown in notes) and thoroughly answer the question of interest.
Part II. In 1978 congress established a Gas Guzzler Tax to discourage the production and purchase of fuel-inefficient vehicles. Every vehicle currently produced is labeled as a Guzzler if its fuel efficiency in MPG is below a certain amount. Trucks, SUVs and Minivans were uncommon in 1978 so are exempt from the Tax. If interested, read more: https://www.epa.gov/fueleconomy/guzzler/
Each vehicle in the data set EpaFE2016Data.csv has a projected Five Year Fuel Cost that estimates how much more or less the fuel cost will be in comparison to the average for similar makes and models. For example, the Honda Fit has a five year fuel cost of -$2750. This implies it is $2750 less expensive over five years to fuel versus the typical vehicle in its class.
Using the data set EpaFE2016Data.csv, compare the five year fuel cost fuel cost in dollars among the 2015 vehicles that are flagged as Guzzlers and Non-Guzzlers.
Use the R code and instructions under Data Analysis 4 link in Canvas to obtain descriptive statistics, a side by side box plot and results from a two sample t test.
a. Include a side-by-side box plot of the data. Is there visual evidence that the five year fuel cost is different between the Guzzler and Non-Guzzler vehicles? Explain.
b. Provide an organized table of the summary statistics. Include the sample means, standard deviations and sample sizes for each group.
c. What type of vehicles are guzzlers? Which vehicle has the highest five year fuel cost?
Do these data provide strong evidence of a difference between the average five year fuel costfor Guzzlers and Non-Guzzlers?
Assume that conditions for inference are satisfied. Use a significance level of 0.10.
d. State the null and alternative hypothesis to answer the question of interest.
e. From the summary statistics, calculate the test statistic and degrees of freedom "by hand". Show work. Conservative degrees of freedom are okay.
f. Obtain a p-value based on your calculated test statistic and degrees of freedom from a t table. (You may use either method to get your df). Show work.
g. From the summary statistics, calculate the 90% Confidence Interval "by hand". Show work.
h. Obtain a p-value from t test and confidence interval using R. Paste the output. Are your answers different? Why, yes/no?
i. Using the R output (from g) give a four part conclusion(shown in notes) and thoroughly answer the question of interest.
Part III. Burning fuel fossils contributes to greenhouse gases in the atmosphere. Included in the EPA analysis of 2016 vehicles israting for greenhouse gas emissions (GHGrating). Compare the greenhouse gas rating among vehicles that use different fuel types. Reference Part I for the description of the four fuel types.
Use the R code under the Data Analysis #4 Instructions to obtain graphical display, perform a Single Factor ANOVA F TEST and test of multiple comparisons.
a. From the side-by-side box plot does there look to be a difference in the average GHG rating among the different fuel types? Include the plot and explain your reasoning.
Does the EPA data provide evidence of a difference between at least one average fuel efficiencybetween the five different drive types? If so, which are statistically different?
Assume that conditions for inference are satisfied. Use a significance level of 0.05.
b. State the appropriate null and alternative hypothesis for the ANOVA F test.
c. Use the F statistic and p-value from the ANOVA table to state whether there is a significant difference between at least two of thefuel typesaverage GHG rating.
a. Paste R output.
b. Include a statement in regards to your significance level.
c. Include a statement in terms of the strength of evidence in terms of the alternative.
d. Using the Tukey's Multiple Comparison procedure output. Are there any individual comparisons that are significant at the 0.05 significance level?
a. Paste R output.
b. List all comparisons that are significant (or state those that are not). Which significant comparison has the largest difference in GHG rating? Give the difference estimate.