What is the rejection region for a two tailed test when a=0.05?
a. [z] > 2.575
b. z>2.575
c. [z] > 1.96
d. [z]>1.645
A two-tailed test of a=0.05 is equivalent to two tests of a=0.05/2=0.025 for each for the upper and lower tails.
So for |z|>1.96 has a=0.025 (two tailed) is equivalent to z>1.96 and z<-1.96.
Ref:
http://www.math.unb.ca/~knight/utility/NormTble.htm
To find the rejection region for a two-tailed test with a significance level (α) of 0.05, we need to determine the critical values on both ends of the distribution curve. These critical values define the boundaries of the rejection region.
In this case, since it is a two-tailed test, we need to split the significance level (α) evenly between the two tails. So, each tail will have an α/2 value of 0.025.
To find the critical value for a standard normal distribution, we can use the z-table or a calculator.
The correct answer is c. [z] > 1.96.
Using the z-table or a calculator, we can find that the z-score that corresponds to an area of 0.025 in one tail is approximately 1.96. For a two-tailed test, we need to consider both tails, so we have a rejection region in the upper tail and a rejection region in the lower tail.
Hence, the rejection region for a two-tailed test when α=0.05 is [z] > 1.96 (upper tail) and [z] < -1.96 (lower tail).