Now that we got the test-statistic from our sample data, the second crucial parameter that we need is the level of significance or alpha (α). Let’s understand this in the next video
So the level of significance or alpha (α) is the maximum permissible limit to which the sample can deviate and for the given test we took it as 0.05. Using this, we can find the critical region for the given test conditions, let’s hear it from rahim.
As you saw in the video, for finding the critical region, you need to use the value of alpha (α) as well as the given null hypothesis. Since it is a two-tailed test, the critical regions would lie on both the sides of the distribution. With the given level of significance at 0.05, the critical region is between -1.960 and +1.960 . So how did we arrive at this value? Since it is a two tail test the probability value will be as follows:
p−value(Area under the curve)=1.0−(α/2)=1−0.025=0.975
The corresponding Z value for 0.975 is +1.960. Since normal distribution curves are symmetrical along the axis both the left and right side value will be -1.960 and +1.960.
Thus now, that we have found the critical region, it becomes easier for us to make the final decision based on the given hypothesis. Let’s get to that in the next segment.