Stats 4590
                    Statistics of Automobile Models

 We will take a look at the following data set, which contains
statistics corresponding to variables and models of various cars. The
data is on 31 models by 11 statistics. It is the datafile "mtcars" in R,
and is saved as a data frame.

 The variables are number of cylinders, displacement (cu.in.),
gross horsepower, rear axle ratio, weight (lb/1000), 
1/4 mile time, 	V/S, transmission (0 = automatic, 1 = manual),
number of forward gears and number of carburetors.  If you're asking "What's a
carburetor?", this is an old data set (from 1974).

 Let's take a look at part of the data: 

> mtcars[1:3,]
               mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4     21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag 21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710    22.8   4  108  93 3.85 2.320 18.61  1  1    4    1

 What variables here are quantitative? Qualitative? Discrete?
Continuous?

 What may be some questions of interest to address with this data?

 In class, we'll look at plots of some of the variables.

> summary(mtcars$mpg) # Summary of miles per gallon

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  10.40   15.42   19.20   20.09   22.80   33.90 

> var(mtcars$mpg) # Variance of mileage
[1] 36.3241
> sqrt(var(mtcars$mpg)) # Standard deviation of mileage
[1] 6.026948

> summary(mtcars$am) # Do all of these values have meaning?
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.4062  1.0000  1.0000 


 Suppose that the automobile manufacturers claimed that their new models
were now more fuel efficient, and were getting more than 19 miles/gal,
on average. Is there any evidence to support this claim?

> t.test(mtcars$mpg, alternative = "greater", mu = 19)

	One Sample t-test

data:  mtcars$mpg 
t = 1.0237, df = 31, p-value = 0.1570
alternative hypothesis: true mean is greater than 19 
95 percent confidence interval:
 18.28418      Inf 
sample estimates:
mean of x 
 20.09062

 > t.test(mtcars$mpg, mu = 19)

	One Sample t-test

data:  mtcars$mpg 
t = 1.0237, df = 31, p-value = 0.3139
alternative hypothesis: true mean is not equal to 19 
95 percent confidence interval:
 17.91768 22.26357 
sample estimates:
mean of x 
 20.09062 


 What type of conclusions can be drawn? What is our scope of inference?