Hypothesis Testing - 2 - Research Aptitude Notes

Process of Hypothesis Testing

• The assumption is the Null hypothesis (H0 ), and it is tested against some Alternative hypothesis (H1 ).
• Statistical tests of the hypothesis are applied to sample data.
• The procedure involved in testing a hypothesis is
  • select a sample and collect the data. 
  • convert the variables or attributes into a statistical form such as mean, proportion.
  • formulate hypotheses. 
  • select an appropriate test for the data such as t-test, Z-test.
  • perform computations.
  • finally draw the inference of accepting or rejecting the null hypothesis. 

Let’s try to understand the process of Hypothesis testing with the help of an example :  

Assume that a radio station selects the music it plays based on the assumption that :

To determine whether this assumption is valid, a hypothesis test could be conducted with the null hypothesis as
Null hypothesis (H0): µ = 30 and
Alternative hypothesis as H1: µ ≠ 30.

• Based on a sample of individuals from the listening audience, the sample mean age, ‘X’, can be computed and used to determine whether there is sufficient statistical evidence to reject H0. 
• Conceptually, a value of the sample mean that is “close” to 30 is consistent with the null hypothesis, while a value of the sample mean that is “not close” to 30 provides support for the alternative hypothesis. 
• What is considered “close” and “not close” is determined by using the sampling distribution of ‘X’.
• Ideally, the hypothesis-testing procedure leads to the acceptance of H0 when H0 is true and the rejection of H0 when H0 is false. 
• Unfortunately, since hypothesis tests are based on sample information, the possibility of errors must be considered.