Find the critical value za/2 that corresponds to the given confidence level.
96%
There isn’t any data lacking. This is the information we are given.
To find the critical value zα/2 for a 96% confidence level, you need to split the remaining 4% in half (since it is a two-tailed distribution).
Since you are looking for a z-value, and assuming a standard normal distribution, the area under the curve beyond zα/2 on both sides will be equal to 2%.
Looking up the z-score in a standard normal distribution table or using a calculator, you will find that the z-value corresponding to an area of 0.02 is approximately 2.05.
Therefore, the critical value zα/2 for a 96% confidence level is approximately 2.05.
To find the critical value za/2 that corresponds to a certain confidence level, you can follow these steps:
Step 1: Determine the confidence level (expressed as a decimal). In this case, the confidence level is 96%, which is equivalent to 0.96.
Step 2: Determine the value of (1 - confidence level). In this case, (1 - 0.96) = 0.04.
Step 3: Divide the value from Step 2 by 2 to find the tail area. In this case, 0.04/2 = 0.02.
Step 4: Look up the tail area in the standard normal distribution table (also known as the z-table) or use a statistical software.
In our case, we want to find the critical value za/2 corresponding to a tail area of 0.02.
Looking up 0.02 in the z-table, we find that the critical value za/2 is approximately -2.05.
Therefore, the critical value za/2 that corresponds to a 96% confidence level is approximately -2.05.