The following data was obtained from 6 months of traffic accident records in the north direction and the south direction of the NJ turnpike. The variable "total number of fatal and non-fatal crashes" was recorded. The data is:

MonthNorthBoundSouthBound

July3734

August3930

September2827

October 1911

November14 3

December2519

Using this data, we would like to check if the average number of crashes is the same for northbound and southbound traffic.

a.What kind of test do you need to perform? and which calculation is needed to obtain the derived variable used to perform the test? Draw a normal probability plot of the derived variable and comment on the plot, is it skewed? heavy tailed? approximately normally distributed? The R functions used to build the plot are qqnorm() and qqline().

b.Assume that the normal probability plot shows that the variable is approximately normal and perform the appropriate test at a significance level alpha of 0.1. Please perform the test and state your conclusion.