Exercise 1: Descriptive Statistics (20 points) a) Create a combined mpg variable called MPG_Combo which combines 60% of

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Exercise 1: Descriptive Statistics (20
points)
a) Create a combined mpg variable called
MPG_Combo which combines 60% of the
MPG_City and 40% of the
MPG_Highway. Obtain a box plot for
MPG_Combo and comment on what the plot tells us
about fuel efficiencies.
b) Obtain box plots for MPG_Combo by
Type and comment on any differences you notice
between the different vehicle types combined fuel efficiency.
A review of the data above suggest that fuel efficiency may
differ by vehicle type. The data suggest that vehicles such as
“Sedans” and “Wagons” enjoy better fuel efficiency with an average
of approximately 24 miles per gallon (Table 2). While “Sports”,
“SUVs” and “Trucks” average approximately 21 and 18 miles per
gallon respectively (Table 2). The data also states that the
optimum fuel efficient vehicle type is a Sedan (40 mpg) and the
least fuel efficient is an SUV (11 mpg).
c) Obtain basic descriptive statistics for
Horsepower for all vehicles. Comment on any
general features and statistics of the data. Use visual and
quantitative methods to comment on whether an assumption of
Normality would be reasonable for Horsepower
variable.
d) Use visual and quantitative methods to comment on whether an
assumption of normality would be reasonable for
Horsepower variable by Type,
especially for Sports, SUV, and Truck (i.e.,
check normality of Horsepower from Type of i)
Sprots, ii) SUV, and iii) Truck.
To determine the normality of horsepower by vehicle type we
conducted qualitative analysis specific to Sports, SUVs and Trucks.
We reviewed histograms, boxplots and normality plots to determine
if horsepower by vehicle type was normally distributed. Visually,
each vehicle type did not seem to follow a normal distribution. To
confirm this, we conducted a Shapiro Wilk test for each vehicle
type (Sports, SUV and Truck) and identified that each vehicle type
had a p value of less than 5%. This supports our hypothesis that
horsepower by vehicle type (for Sports, SUV and Truck) does not
follow a normal distribution. Tables 1-11 support our claim.
   
Exercise 2: Hypothesis Testing (15 points)
Perform a hypothesis test of whether SUV has different
horsepower than Truck, and state your conclusions
a) Which test should we perform, and why? Justify your answer
based on findings on Exercise 1 (d).
b) Specify null and alternative hypotheses.
c) State the conclusion based on the test result.
The airquality data will be used for Exercise
3. The information about variables in the dataset can be found in
R.
Exercise 3: Hypothesis Testing (15 points)
Perform a hypothesis test -whether Wind in July has a different
speed (mph) than Wind in August.
a) Which test should we perform, and why? See QQ-plot and
perform Shapiro-Wilk test for normality check.
b) Specify null and alternative hypotheses
c) State the conclusion based on the test result.