1) Descriptive Statistics
a) Central Tendency: Mean, median, mode 
b) Variation: std dev, variance, CV = sd/mean
b) Shape: skewness using histograms: hist()

2) Normal distribution
a) Area finding under the curve: Probabality
of some event. e.g. if we randomly pick up a person
from this group, what are the chances, this person's
age > 25, or salary < 75000, or weight between 150 and
170 lbs. ==> pnorm()

b) Area is given. We wonder cutoff point(s) for area.
==> qnorm()

3) Confidence Intervals
  LowerLimit < mu < UpperLimit
LowerLimit = xbar - z*sd/sqrt(n)  
UpperLimit = xbar + z*sd/sqrt(n)

90% confidence level -> z=1.68
95% confidence level -> z=1.96
99% confidence level -> z=2.58
For example: qnorm(0.95) = 1.68

4) Hypothesis testing - One sample
   Two sided (mu = A or not)

a) Construct your hypothesis
   H0: mu = A
   Ha: mu != A
b) i) Calculate zcrit and zstat using formulas.
      Sketch and look at zstat's position in the distribution.
   ii) Use t.test() function. Look at the pvalue.

5) Hypothesis testing - One sample
   One sided (mu > A or not)
a) Construct your hypothesis
   H0: mu <= A
   Ha: mu > A
   H0: mu >= A
   Ha: mu < A
b) Same procedure as in two sided except
   don't divide alpha by 2.
   If question is ">", shade the right tail.
   If question is "<", shade the left tail.

6) Hypothesis testing - Two samples
   a) Paired t-test: t.test(..., paired = TRUE, ..)
   b) Equal variances: t-test(..., var.equal = TRUE,..)
   c) Seperate variances t-test: t-test(..., var.equal = FALSE,..)
   Look at the pvalue, if it is less than alpha/2, then reject H0.

7) z-test for proportions
   One categorical variable. Test claims about the proportion
   of one category. e.g. Proportion of voters supporting 
   candidate A is equal to 55%. 
   Majority: 50% or more supporting candidate A.

8) Chi-Square test for independence
   Two categorical variables. Test if these two variables
   are independent or not. Use the chi.square() and look at pvalue.
   If pvalue < alpha, reject H0 which says they are independent.

9) ANOVA F test
   One numerical and One categorical variable.
   You are testing if the mean of the numerical variable differentiate
   along the categories of the categorical variable.
   H0: mu1 = mu2 = mu3 .... = mun
   Ha: At least one mean is different.
   Use function aov() and look at pvalue to see if you can reject H0.
 
10) Linear Regression
    Simple Lin. Regression: Y = b0 + b1*X
    Multiple Linear Regression: Y = b0 + b2*X1 + b2*X2 + ... + bn*Xn
    Calculate b coefficients using lm() function.  
    Make sure the model is a good fit. 
    Understand what each coefficient means.