What is the p value and how do we calculate it?

Lets assume we are doing a 5% two-tailed test, so the critical Z score will be +/- 1.96.  If our test stat = 1.8 then we could not reject the null at 5% significance (or 95% confidence)

If instead we did a 10% significance test (or 90% confidence) then the critical value would be 1.645 so we would reject the null since the test stat is greater than the critical stat

So at 10% we can reject but at 5% we cannot.  The p value is the cut-off point.

If you look up in a normal table 1.8 you get a probability of 0.4641 which means the area to the right must be 0.5-0.4641 = 0.0359.

Therefore the lowest significance level (for a two-tail test) where we can reject the null is 2 x 0.0359 = 7.18%