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

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Enlighten_me

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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.
 
S2000magician wrote:
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.
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Got it. Thanks a lot.
 
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