Hypothesis Testing
       Introduction
       • In this session we will see
           •   What a hypothesis test is
           •   What a p-value is
           •   What a t-test is
       • This is intented for first stages in Statistics Students
       • Previous knowledge: descriptive statistics, random 
          variables, distributions
             Hypothesis Testing
       What is a hypothesis test:
       • A formal way to statistically test a theoretical 
           assumption based on the data we have.
       • Key concepts:
            •  Null hypothesis H0 : The prediction we usually get 
               information if rejecting
            •  Alternative Hypothesis H1
            •  Significance level α : The probability of rejecting Ho 
               when it is true (Type I error, false positive)
    Hypothesis Testing
   Why do we need it?
   • Is there a significant difference between two 
    populations?
   • Is there a significant relationship between two 
    variables?
   • Is the mean bigger , smaller or different from a 
    given value?
    Hypothesis Testing
   •  
   A simple example
   • We will examine the steps of hypothesis testing 
    through a general example:
   • Assume we have n data from two different 
    populations A and B,
   ,…, with sample mean  and,
   ,…, with sample mean 
    Hypothesis Testing
   A simple Example:
   • We are interested to know whether there 
   are significant differences between the two 
   populations or not. 
   • To answer this question, we need to perform 
   a statistical test.