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Hypothesis Testing - 2 - Research Aptitude Notes

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Process of Hypothesis Testing

Testing of a hypothesis is done by using statistical methods. Testing is used to accept or reject an assumption or hypothesis about a random variable using a sample from the distribution.

Hypothesis Testing - 2 - Research Aptitude Notes

  • 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 :

‘the average age of its listening audience is 30 years’.

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.
 
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