Math Help - Z-tables, Backwards and Interpolation: I just don't get it.

1. Z-tables, Backwards and Interpolation: I just don't get it.

I swear, every time I think I get it, I end up being completely wrong. Basically, I'm still confused as to how $Z_{0.01}=2.326$, or $Z_{0.025}=1.96$, or this:

How did $z_{a/2}$ become 2.575? I understand that
$1-a=0.99$
$a=0.01$
$a/2=0.005$

...but not how that transforms into 2.575.

2. Originally Posted by trackies
I swear, every time I think I get it, I end up being completely wrong. Basically, I'm still confused as to how $Z_{0.01}=2.326$, or $Z_{0.025}=1.96$, or this:

How did $z_{a/2}$ become 2.575? I understand that
$1-a=0.99$
$a=0.01$
$a/2=0.005$

...but not how that transforms into 2.575.
Pr(z > z*) = 0.005 => Pr(z < z*) = 1 - 0.005 = 0.995.

So find 0.995 and go backwards to the coreesponding value of z:

So z* = 2.575 (using tables).

3. My z table only goes down to 3.0 on the side, and 0.09 along the top, so I can't find .995.

4. Originally Posted by trackies
My z table only goes down to 3.0 on the side, and 0.09 along the top, so I can't find .995.
No, those are the z-values. You are looking for the z value corresponding to 0.995 .... Look for 0.995 in the big array of numbers corresponding to probabilities ..... Then look at what value of z gives it .....

5. Ah, no, that's what I mean. The largest number of the z-table given to us is 0.4990, which corresponds to the z-value 3.09. That's why 0.995 isn't on this table..

6. Originally Posted by trackies
Ah, no, that's what I mean. The largest number of the z-table given to us is 0.4990, which corresponds to the z-value 3.09. That's why 0.995 isn't on this table..
There are (at least) two types of normal table one gives the area under the curve from -infty to z, and the other the area from 0 to z (z>0). You want the former, but you can get the numbers by using the table you have got but subtracting 0.5 of off the p value (this is because the area from -infty to 0 is exactly 1/2).

So in this case you want to use p=0.995-0.5=0.495

RonL