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Calculator Z score
Now that you know how to calculate the Z score for a given percentage by using the Z table, (as we learnt in this earlier post ),
in this post we will look into how to calculate Z score in different scenarios.
For example, if I say the significance level of a two tailed test is 10%.
Then how will you calculate the Z score?
What will you look up in the Z table?
Since it is a two tailed test, it would mean there are two critical regions. (as shown with red area in the image below).
Now, the area of these two red regions together is what is the significance level. (ie. 10%).
So, one area (the left hand side red region) would be 10/2 = 5%.
Hence, to find the Z-score for this critical region (the left side) you would look up 5% on the Z table to get the corresponding Z score.
However, what would you look up in the Z-table for the critical region on the right hand side?
Many people make the mistake of looking up 5% for this side as well.
But, that is NOT correct.
You need to keep in mind, that the percentage that we look up in the z table is the percentage of area covered in the graph from the LEFTMOST of the graph.
For the critical region on the right hand side (right side red area),
you would have to look up
100 - 5 = 95%
on the Z table.
Now, think about the following scenarios:
1. What would you look up in the z- table to calculate the Z score for a one tailed test (Lower Tailed Test)?
2. What would you look up in the z- table to calculate the Z score for a one tailed test (Upper Tailed Test)?
Significane level being 10% in both cases.
Pause and think about it before you read through the answers below.
In the first case, you would look up 10% on the z table.
Since it is a lower tailed test, the entire critical region would be on the left hand side.
Thus the area of the graph from the leftmost (starting point) upto the point where the critical region ends is 10%.
However, in the second case of Upper tailed test, this area of 10% is on the right hand side.
Thus the area from the start of the graph upto the point of the critical region would be 100 - 10 = 90%.
Hence you would look up 90% in the z table for this scenario.
