Why Hypothesis Testing?

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Right-tail test. Ha is more probable. Left-tail test. Ha is more probable. In the examples, the parameter is mu and the sampling distribution is normal. When testing other parameters, the same 3 types of tests are used. The category for the test is the region in which the null hypothesis is likely to be rejected and the alternative hypothesis is more probable. Ha is more probable. Two-tail test.

What is Hypothesis?

In a laymen language, when we want to differentiate whether the result from the sample is by chance or can we draw more meaningful inferences from it.

Hypothesis Test – is a method of Statistical inference.  In order to check if a statistical hypothesis is true we would have to examine the entire population (which is impractical) we examine a random sample from the population. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.

Let us understand this with the help on an example.

Suppose XYZ School claims that the average marks in Geography for the Student’s of class10 in 75. Now, when we pick a random sample of 30 students, the average marks are 63.do we have enough evidence to say that the claim is incorrect?

Stating Hypothesis:

  •  Null Hypothesis states what we think is wrong with the problem. i.e. in this case we think the claim is correct and the sample results were by chance.
  •  Alternate Hypothesis states what we think is wrong with the Null Hypothesis. i.e. in this case we think the claim is incorrect. There is a significant difference between the result of the sample and population

 

Testing Hypothesis:

  • Once you have set up the ‘Null Hypothesis’ and the ‘Alternate Hypothesis’ such that they are mutually exclusive. We need to check whether they are true or not.
  • Second, we set up a significance level. Based on the ‘Level of Significance’ we accept or reject the Null Hypothesis.
  • Thirdly, compute the Test- statistics that would help to determine the results.
  • Fourthly, Make Decision to accept the Null Hypothesis or not.

Once we have taken a decision there can alternative scenarios to that decision.

 

Hypothesis Decision:

Decisions Predicted from Hypothesis
Accept Reject
Actual Accept Correct Type I Error
Reject Type I Error Correct
  • Type I error. A Type I error occurs when we rejects a null hypothesis when it is true or a False Alarm that was raised. The probability of committing a Type I error is called the significance level.
  • Type II error. A Type II error occurs when we fails to reject a null hypothesis that is false. The probability of committing a Type II error is also said to be a Missed Opportunity. The probability of not committing a Type II error is called the Powerof the test.

 

When we make decision rules for Accepting the Null Hypothesis or not, we do this with reference to the P-Value

P-value- is the maximum chance that I am willing to take for a Type 1 error.  If the P-value is less than the significance level, we reject the null hypothesis.

 

One-Tailed and Two-Tailed Tests

Statistical hypothesis, where the region of rejection is on only one side of the sampling distribution, is called a one-tailed test. For example, suppose the null hypothesis states that the mean is less than or equal to 75. The alternative hypothesis would be that the mean is greater than 75. The region of rejection would consist of numbers located on the right side of sampling distribution; that is, a set of numbers greater than 75.

Statistical hypothesis, where the region of rejection is on both sides of the sampling distribution, is called a two-tailed test. For example, suppose the null hypothesis states that the mean is equal to 75. The alternative hypothesis would be that the mean is less than 75 or greater than 75. The region of rejection would consist of numbers located on both sides of sampling distribution; that is, the region of rejection would consist partly of numbers that were less than 75 and partly of numbers that were greater than 75.

 

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