Conceptually understand z-score obtained from standard normal table

Asked Dec 10 '20 at 22:47

Active Dec 10 '20 at 22:47

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I am trying to conceptually understand the following …

For a two-sided test … alpha = 5%, gives z-score = 1.96 (i.e. you have 95% probability between tails)

But for a one-sided tested … alpha = 5%, i.e., you have 97.5% probability between tails, why z-score be 1.65? I mean you have higher probability, so I don’t understand why z-score would be lower than that of a two-sided test.

Any help to understand this will be appreciated.

asked Dec 10 '20 at 22:47

F0l0w

For much more about this, search our site for 'two tail* test Z score'. – whuber Dec 10 '20 at 22:55
it is easier to look at in terms of what is actually at one of the tails. For the two sided alpha=5% that means there is only 2.5% at each tail. So when you look at the z-table you would find the probability of 97.5%. However for a one-sided, we want 5% at the tail so we look for 95% on the table. This is why we get a lower z value – user593295 Dec 10 '20 at 23:35
Thanks, that makes sense – F0l0w Dec 11 '20 at 18:45

Conceptually understand z-score obtained from standard normal table

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