Given the same level of significance, are the z values in one tailed and two tailed test different?

Hi! I am currently reading the hypothesis portion of quant methods. I am confuse whether there is a difference in the z value in one tailed test and two tailed test given the same level of significance or whether this is a mistake? These are the given: 1. Two tailed test 2. 5% level of significance Therefore, z value=1.96 However, given 1. One tailed test 2. 5% level of significance z-value= 1.65(from what I remember, 1.65 is for 10% level of significance) Please explain.

They’re different.

At the 5% level of significance:

  • For a 1-tail test, 5% probability is included in only one tail, so the z-value to get to that level is 1.645. This is the same z-value for a 2-tail test at the 10% level of significance (5% in each tail).
  • For a 2-tail test, 2.5% probability is included in the left tail, and 2.5% probability in the right tail, for a total of 5%; the z-value to get 2.5% in each tail is 1.96. This is the same z-value for a 1-tail test at the 2.5% level of significance.

Got it. Thanks a lot.

Por nada.

Interesante :slight_smile: