Hypothesis Testing

What is hypothesis?

Hypothesis is a claim about the Population parameter such as Mean, Standard Deviation or Proportion etc. It’s a claim we can test, suppose the average age of the students in the city is 23.

This becomes the Null hypothes is  average Age of Students = 23, we have assigned this claim to the null hypothesis as it has equality sign.The Alternative hypothesis becomes the opposite , average Age of Students ≠ 23. 

We utilize this hypothesis for a TWO TAIL TEST, because Alternative hypothesis basically means that Average Age of students is either more or less than 23.

Suppose if we test that the population mean µ<23, now this claim does not have equality sign, we will make it as an Alternative Hypothesis , now we will formulate the null hypothesis  that population mean µ≥23. This hypothesis will be used for performing a ONE TAIL TEST. This is a left tailed hypothesis

And similarly, if we test that the population mean µ>23, we will make it an Alternative Hypothesis, and the Null hypothesis will be that the population mean will be µ≤23. This is known as Right Tailed Test.

We either accept or reject the null hypothesis, when we reject the Null hypothesis, we say that we do NOT HAVE enough evidence to support the alternative hypothesis, and when we accept the null hypotheses, we say that we do HAVE enough evidence to support our Alternative hypothesis.

Now the question arises how and when do we reject or accept the null hypothesis? We set the rejection region using “Significance Level” or α. We then perform a Test Statistic, and if that test statistic falls in the rejection region we reject the null hypothesis.

 

The significance level mostly or  used is 0.05%, the other significance levels are 0.01% or 0.1%.  The significance level or α specifies the Rejection Region, and the null hypothesis in this region should be rejected.

In a two tailed test, rejection region is near the tails of the normal distribution, it is denoted by, and if the test statistic (Z-score) falls in the rejection region we reject the null hypothesis. The rejection region is also known as critical region.

Z score and z – test are different, they are not the same, to calculate the rejection region we require z test using significance level , and Z score is the standardized score, where the distribution has mean 0 amd standarad deviation is 1. When the population variance is not known and the sample is small then we use t-test instead of z test. 

The rejection region is determined if the test is two tail or one tail, when we are performing two tail tests, we will divide α by 2. Suppose we are using 0.05% as the alpha value then the value becomes 0.0250, and by checking z standard table we get a value of 1.96.  If the Z score > 1.96, this means that the statistic lies in the rejection region and we will reject the null hypothesis.

In the Same way we perform one tail test using the value of α to determine the rejection region and again if the Z score falls in the rejection region we reject the null hypothesis.

We employ the t statistic if the population variance is not known and use sample standard deviation, however some where you will also see people performing z-statistics due to Central Limit Theorem , and taking sample>=30, even if the population variance is known or not known.

We will continue about Type I  and Type II error and the p-value in the next blog. Stay tuned!.