I don't understand where you got 1.96 in this problem

Question

Hi,

I am totally confused how to find z - which table to get it from or which formula to use in which calculator for confidence intervals. I am guessing it is confidence intervals that is being asked for. Any help you can give would be appreciated.

Answer 1

Hi Kathleen,

Here's a quick list of common z-critical values for 2-sided confidence intervals:

95% confidence interval: +/-1.96

90% confidence interval: +/- 1.645

99% confidence interval: +/- 2.575

I would recommend committing these values to memory, but if you want to get from z-table, do the following:

Subtract your confidence level from 1 and divide by 2. For example, if you have 95% confidence, you would do:

(1-0.95)/2=0.025

Then take 1 minus the result and look for that value in the interior of the z-table.

(1-0.025)=0.975

From z-table, z_0.975=1.96

As far as which table to get z from, just search online for "z score table" and one should come up. Most statistics textbooks will also have a table as an appendix.

Now, to the last part of your question, a formula for z-confidence intervals:

CI=x-bar +/- z*SE

Breaking this down,

CI=confidence interval

x-bar=sample mean, usually given

z*=z-critical value, will likely be one of the values mentioned above for 90, 95, or 99% confidence

SE=standard error, which has its own calculation and formula

SE=sigma/sqrt(n)

sigma=population standard deviation

n=sample size

Once you have all of these, you can compute a z-confidence interval. Note that you must have known population standard deviation to do this. I hope this helps.