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ANATOMY OF OBTAINING za/2
For a value of za/2 the subscript represents an area in the tails of the standard normal curve and za is the area in the right tail. These values
are used within confidence interval formulas.
Example:
Areas under the Curve:
Suppose we want to construct a 100(1 – a) = 95% confidence
interval for m.
For a (1 – a)100% confidence level, the area between –z and +z
is (1 - a).
1 - .95 = .05, therefore a = .05 and a/2 = .025.
Because the total area under the normal curve is 1.0, the total
area under the curve in the two tails is a. This is called the
significance level. Here in our example a = 1 - .95 = .05.
We will need to find z.025. That is, we need to find the z-score
with area .025 to its right.
Therefore, as shown below, the area under the curve in each of
the two tails is a/2 = .025
For a Standard Normal Table that gives us all of the area to the
left of a specified z-score, we will subtract .025 from 1 to obtain
.9750. We will now look in the “body” of our table to find .9750
(or the closest value to it). The z-score with area .9750 to its left
(and .025 to its right) is 1.96. Then, using the symmetry of the
curve, the z-score with area .025 to its left is -1.96. (This process
will vary slightly depending on the type standard normal table
being used.)
.9500
.025
-1.96
1.96
a/2
(1  a )
.025
.025
z
z
.9500
a/2
.025
-z
z
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