During hypothesis testing, we need to judge whether we need One Tailed Test or Two Tailed Test to calculate the p-value and critical value. Therefore, we select or reject the null hypothesis based on whether our test is one-tailed or two-tailed.
Our claim during hypothesis testing is an input to know whether the type of test is one tailed or two tailed?
It is important to determine whether the test is two-tailed or one-tailed before conducting the significance tests(T-Test, Z-test, U-Test)
A two-tailed test determines if there is a significant difference between the sample and the population. In other words, the parameter in discussion can be greater or less than the specified value.
As shown in the above image, the critical region has two parts at both ends of the curve. A two-tailed test is a directionless test because it does not specify any defined direction. In other words, the specified parameter can be greater than or less than the mean value.
Example of two tailed test
Problem Statement: Check whether the part weight manufactured from machine is equal to 15 grams.
Null Hypothesis: The mean part weight is equal to 15 grams.
Alternative Hypothesis: The mean weight of the part is not equal to the 15 grams.
If you look at the above example, In alternative hypothesis the part weight can be greater or less than 15 grams. Therefore it is a two tailed test.
One tailed Test
A one tailed test determines if the mean value of the specified parameter from the sample is significantly greater or less than the population.
As shown in the above image, the critical region in the one-tailed test is on one side. It can be either left-tailed or right-tailed. A one-tailed has a defined direction. In other words, the specified parameter can be either greater than or less than the mean value.
Therefore, we can classify one-tailed test into two types:
- Left tailed test
- Right tailed test
In the left-tailed test, the critical region lies in the extreme left of the curve. It is equal to alpha.
In the right-tailed test, the critical region lies in the extreme right of the curve. It is equal to alpha.
Example of one tailed test
Problem Statement: Check whether the part weight manufactured from machine is less than 15 grams.
Null Hypothesis: The mean part weight is greater than or equal to 15 grams.
Alternative Hypothesis: The mean weight of the part is less than 15 grams.
If you look at the above example, In alternative hypothesis the part weight can be less than 15 grams. It can not be greater than 15 grams. Therefore it is a left tailed test.