ANATOMY OF OBTAINING z a /2

1. ANATOMY OF OBTAINING za/2 For a value of za/2the 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: Suppose we want to construct a 100(1 – a) = 95% confidence interval for m. 1 - .95 = .05, therefore a = .05 and a/2 = .025. We will need to find z.025. That is, we need to find the z-score with area .025 to its right. Areas under the Curve: For a (1 – a)100% confidence level, the area between –z and +z is (1 - a). 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. 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 .9500 .025 .025 .025 .025 z -z z z -1.96 1.96