Find Critical Value of t for One or Two Tailed Z-Test

Standard normal-distribution table & how to use instructions to find the critical value of Z at a stated level of significance (α) for the test of hypothesis in statistics & probability surveys or experiments to large samples of normally distributed data. It's generally represented by Z_e. The estimated value of Z or Z-statistic (Z₀) is compared to critical value of Z from standard normal-distribution table to check if the null hypothesis in the Z-test is accepted or rejected at a specified level of significance (α). For locating the Z_e (critical value of Z) in the table quickly, users can supply the values of Z-score in the above interface. This Z-table to find the critical value of Z is also available in pdf format too, users may download this table in pdf format to refer it later offline.

The negative & positive z-scores lies on the left & right side of the mean of standard normal distribution respectively. It means that the negative z-score lies on left side represents the left tail & the positive score lies on right side represents right tail of the distribution.

How to Find Critical Region in Z-Test

Users may use this one or two tailed z-table calculator or refer the rows & columns value of standard normal distribution table to find the critical region of z-distribution.
by Using Calculator
For one one (left or right) tailed Z-test :
Supply the positive or negative value of z-score to find the rejection region right or left to the mean of normal distribution respectively.

For one two tailed Z-test :
Supply the positive & negative values of the z-score to find the rejection region at both right and left side of the mean of normal distribution.

by Using Normal-Distribution Table
Z-scores generally ranges from -3.99 to 0 on the left side and 0 to 3.99 on the right side of the mean. Refer the column & row values for z-score. The point where the row & column meets for the corresponding z-score value is the critical value of Z or the rejection area of one or two tailed z-distribution. For example the -2.95 < Z is the left tailed distribution.
To find the probability of z-score, refer the column value for -2.9 and row value for 0.05 in the negative values of standard normal distribution. The point where the column & row values met at 0.0016 is the probability or critical value of Z.
Similarly for two tailed Z-test,
-1.73 < Z < 2.25 is the two tailed distribution.
To find the probability of z-score,

1. Refer the column value for -1.7 and row value for 0.03 in the negative values of standard normal distribution to find the left tail. Therefore, the critical (rejection region) value of Z on left side is 0.0418
2. Similarly refer column value for -2.2 and row value for 0.05 in the positive values of standard normal distribution to find the right tail. Therefore, the critical (rejection region) value of Z on right side is 0.9878
3. Find the difference between left & right tail critical values of Z
4. The modulus of difference between both left & right side values is the probability of two tailed Z-score values.

Inference

The below statements show when to accept or reject null hypothesis H₀ in one or two tailed Z-test

For null hypothesis H₀ for Z-test :
If Z₀ < Z_e then the null hypothesis H₀ is accepted.
It states that there is no significance difference between Z-statistic & expected value of Z.

If Z₀ > Z_e then the null hypothesis H₀ is rejected.
It states that there is significance difference between Z-statistic & expected value of Z.