You either look it up in a table of z scores or you can use a calculator such as the TI8 and use normalcdf.
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Normally you would find the critical value when given the p value and the test statistic.
Assume the z-score is relative to zero score. In simple terms, assume that we have 0 < z < z0, where z0 is the arbitrary value. Then, a negative z-score can be greater than a positive z-score (yes). How? Determine the probability of P(-2 < z < 0) and P(0 < z < 1). Then, by checking the z-value table, you should get: P(-2 < z < 0) ≈ 0.47725 P(0 < z < 1) ≈ 0.341345
You will need to use tables of z-score or a z-score calculator. You cannot derive the value analytically.The required z-score is 0.524401
The p-value is the probability of any event or the level of significance for any statistical test. The z-score is a transformation applied to a Random Variable with any Normal distribution to the Standard Normal distribution.
The answer depends on what the test statistic is: a t-statistic, z-score, chi square of something else.