Thread: Problem figuring out the Z-score of 95%

Hello all,

We're currently doing problems on confidence intervals, and for the problem I'm doing I have to find the 95% confidence intervals for a problem. I know I have to enter the z-score in the equation mean+or- z x (standard error)
I have noticed in class that whenever we have to construct 95% confidence interval the professor would put the z-score of 1.96. However I just checked the z-score table and when I looked up .9500 it had a z-score of 1.645 ....what's going on here? I don't know if I missed something and there is a reason why we're using 1.96 when according the z table that constructs 97.5%, or maybe I'm doing something wrong. Also it's a dummy variable for this equation, if that has anything to do with it. Which one should I use? Is my professor wrong for some reason? Would a 95% confidence interval use the z-score of 1.96 or 1.645? Thank you.

Remember that when you are constructing confidence intervals, you have $\displaystyle (1-\alpha)$ and $\displaystyle \alpha/2$ at each end. Therefore, for a 95% confidence interval, you want +/- 2.5% at each end, not 5% as your interval would construct. Thus, your professor is correct.

Originally Posted by jesserz

Hello all,

We're currently doing problems on confidence intervals, and for the problem I'm doing I have to find the 95% confidence intervals for a problem. I know I have to enter the z-score in the equation mean+or- z x (standard error)
I have noticed in class that whenever we have to construct 95% confidence interval the professor would put the z-score of 1.96. However I just checked the z-score table and when I looked up .9500 it had a z-score of 1.645 ....what's going on here? I don't know if I missed something and there is a reason why we're using 1.96 when according the z table that constructs 97.5%, or maybe I'm doing something wrong. Also it's a dummy variable for this equation, if that has anything to do with it. Which one should I use? Is my professor wrong for some reason? Would a 95% confidence interval use the z-score of 1.96 or 1.645? Thank you.

Z=1.645 would give you a 90% confidence interval. The table you are looking at is a cdf for the normal distribution, so when it says Z=1.645 corresponds to 5%, it means 5% in the upper tail. By symmetry, Z=-1.645 would have 5% in the left-hand tail as well.