Examine statistical data consisting of records of car accidents on Victorian roads and freeways in 2012. The Victorian department of transportation, Police and VIC Roadsare interested in calculating the main factors affecting car accidents in Victoria. They will use this information to develop strategies aimed at reducing the number of fatalities on Victorian roads.

Alcohol is a major factor in road deaths in Victoria. Each year, about one quarter of drivers killed in road crashes had a blood alcohol concentration (BAC) of .05 or greater.

The Victorian road rules relating to the use of alcohol & drugs by drivers may be briefly summarized as follows:

Blood alcohol concentration

Professional drivers such as truck, bus or taxi drivers must have a blood alcohol concentration (BAC) under 0.02; P-platers and learner drivers, as well as visitors from interstate or overseas, must have a zero blood alcohol concentration (BAC). All other drivers must stay under .05 BAC.  You have to be under .05 BAC while supervising a learner driver. This rule applies to public roads and also private property.

Drug impairment

It is illegal to drive while impaired by any drug whether that drug is legal or illegal.  You must not be affected by illegal drugs while accompanying a learner driver.  This rule applies to public roads and also private property. (VIC Roads, 2012).

Assignment Tasks

For each task below, you must answer all the questions in sequential order and submit all of the required printouts, graphs, tables and summaries required.

NB:Each graph and table should have a heading and each axis should have a label!!

1. Introduction and Variable List: Give a brief introduction to your report.Describe the nature of the data. Read questions 3 to 8 and briefly describe the specific data and relationships which will be examined here.

2. Data: Provide a printout of the data in your sample, sorted in ascending order based onDriver ID number.
Give a brief comment about what you what would happen to the answers to your assignment if you had a different randomly selected sample of size 180.

3. Produce a histogram showing the age distribution of the drivers involved in car accidents. Provide your comments on the graph shape, and the most suitable measures of centre and spread for this data.

4. Pivot Tables:There is a general feeling that male drivers commit more driving offences causing more accidents and more fatalities compared to female drivers. For each of the following prepare a contingency table (cross-classification table), using the Pivot Table option in Excel.Make sure tocomment on similarities or differences and any conclusions you can draw in each case.

a) The average car speed in an accident for the cause of accident split on gender.

b) The average driver blood alcohol level in a road accidentfor each licence type split on gender.

c) The number ofroad accident fatalitiesfor each licence typesplit on gender.

5. T-Test and CI:The Victorian police believe that the average speed of vehicles involved in accidents on Victorian highways is significantly higher than 100 km/hr.

a) Obtainappropriate descriptive statistics and socalculate a 95% confidence interval for the mean car speed in accidents onVictorian highways.

b) Conduct a statistical test to determine if the average car speed in accidents on Victorian highways is significantly higher than 100 km/hr.

6. Stratified scatter plot with trend lines: Obtain a stratified scatterplot comparing the relationship betweendriver age andcar speed (km/hr) in accidentsfor each gender.Think carefully about which variable should go on the vertical axis. Remember, it is the independent variable that goes on the horizontal axis (i.e. the x-axis).  Include trend lines, their equations and R-squared values on the graph. Make sure you label axes properly and that your graph has an appropriate title.                                                                 

Briefly compare the nature of the relationship between these two variables,the driver Age (years) and Speed (km/hr), formales and females(Hint: mention any differences in the slope of the trend line and/or the R-squared values and what this indicates).

7. Create a table of correlation coefficients for the following variables:Age, Number of Fatalities, Car Speed and Blood Alcohol Level. Discuss your results and state which pairs of variables have the highest and the lowest correlation coefficients.

8. Use Excel to carry out a regression analysison the two variables: driver age (years)(independent variable) and car speed (km/hr)(dependent variable).

a) Copy the output into your assignment and use it to determine the answers to the following questions.

b) Write down the regression equation.

c) State the R-squared value and the standard error and explain what they mean with respect to the data.

d) Write down the value of the gradient of the regression line and explain what it means for this data.

e) Are the values for the constant and the gradient (slope) significant (i.e. significantly different from zero) in this case? Justify your answer.

f) Do you think this regression model is a good model? Justify your answer using the regression output.  

9. Using the information obtained for your analyseswrite a short conclusion about what you found from the study above.