# 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 Ze. 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 Ze (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.

Standard Normal Distribution Table for Z = 0.00 to 3.59
Z0.000.010.020.030.040.050.060.070.080.09
0.0 0.50000.50400.50800.51200.51600.51990.52390.52790.53190.5359
0.1 0.53980.54380.54780.55170.55570.55960.56360.56750.57140.5753
0.2 0.57930.58320.58710.59100.59480.59870.60260.60640.61030.6141
0.3 0.61790.62170.62550.62930.63310.63680.64060.64430.64800.6517
0.4 0.65540.65910.66280.66640.67000.67360.67720.68080.68440.6879
0.5 0.69150.69500.69850.70190.70540.70880.71230.71570.71900.7224

0.6 0.72570.72910.73240.73570.73890.74220.74540.74860.75170.7549
0.7 0.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852
0.8 0.78810.79100.79390.79670.79950.80230.80510.80780.81060.8133
0.9 0.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389
1.0 0.84130.84380.84610.84850.85080.85310.85540.85770.85990.8621

1.1 0.86430.86650.86860.87080.87290.87490.87700.87900.88100.8830
1.2 0.88490.88690.88880.89070.89250.89440.89620.89800.89970.9015
1.3 0.90320.90490.90660.90820.90990.91150.91310.91470.91620.9177
1.4 0.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319
1.5 0.93320.93450.93570.93700.93820.93940.94060.94180.94290.9441

1.6 0.94520.94630.94740.94840.94950.95050.95150.95250.95350.9545
1.7 0.95540.95640.95730.95820.95910.95990.96080.96160.96250.9633
1.8 0.96410.96490.96560.96640.96710.96780.96860.96930.96990.9706
1.9 0.97130.97190.97260.97320.97380.97440.97500.97560.97610.9767
2.0 0.97720.97780.97830.97880.97930.97980.98030.98080.98120.9817

2.1 0.98210.98260.98300.98340.98380.98420.98460.98500.98540.9857
2.2 0.98610.98640.98680.98710.98750.98780.98810.98840.98870.9890
2.3 0.98930.98960.98980.99010.99040.99060.99090.99110.99130.9916
2.4 0.99180.99200.99220.99250.99270.99290.99310.99320.99340.9936
2.5 0.99380.99400.99410.99430.99450.99460.99480.99490.99510.9952

2.6 0.99530.99550.99560.99570.99590.99600.99610.99620.99630.9964
2.7 0.99650.99660.99670.99680.99690.99700.99710.99720.99730.9974
2.8 0.99740.99750.99760.99770.99770.99780.99790.99790.99800.9981
2.9 0.99810.99820.99820.99830.99840.99840.99850.99850.99860.9986
3.0 0.99870.99870.99870.99880.99880.99890.99890.99890.99900.9990

3.1 0.99900.99910.99910.99910.99920.99920.99920.99920.99930.9993
3.2 0.99930.99930.99940.99940.99940.99940.99940.99950.99950.9995
3.3 0.99950.99950.99950.99960.99960.99960.99960.99960.99960.9997
3.4 0.99970.99970.99970.99970.99970.99970.99970.99970.99970.9998
3.5 0.99980.99980.99980.99980.99980.99980.99980.99980.99980.9998

Standard Normal Distribution Table for Z = -3.59 to 0.00
Z0.000.010.020.030.040.050.060.070.080.09
-0.0 0.50000.49600.49200.48800.48400.48010.47610.47210.46810.4641
-0.1 0.46020.45620.45220.44830.44430.44040.43640.43250.42860.4247
-0.2 0.42070.41680.41290.40900.40520.40130.39740.39360.38970.3859
-0.3 0.38210.37830.37450.37070.36690.36320.35940.35570.35200.3483
-0.4 0.34460.34090.33720.33360.33000.32640.32280.31920.31560.3121
-0.5 0.30850.30500.30150.29810.29460.29120.28770.28430.28100.2776

-0.6 0.27430.27090.26760.26430.26110.25780.25460.25140.24830.2451
-0.7 0.24200.23890.23580.23270.22960.22660.22360.22060.21770.2148
-0.8 0.21190.20900.20610.20330.20050.19770.19490.19220.18940.1867
-0.9 0.18410.18140.17880.17620.17360.17110.16850.16600.16350.1611
-1.0 0.15870.15620.15390.15150.14920.14690.14460.14230.14010.1379

-1.1 0.13570.13350.13140.12920.12710.12510.12300.12100.11900.1170
-1.2 0.11510.11310.11120.10930.10750.10560.10380.10200.10030.0985
-1.3 0.09680.09510.09340.09180.09010.08850.08690.08530.08380.0823
-1.4 0.08080.07930.07780.07640.07490.07350.07210.07080.06940.0681
-1.5 0.06680.06550.06430.06300.06180.06060.05940.05820.05710.0559

-1.6 0.05480.05370.05260.05160.05050.04950.04850.04750.04650.0455
-1.7 0.04460.04360.04270.04180.04090.04010.03920.03840.03750.0367
-1.8 0.03590.03510.03440.03360.03290.03220.03140.03070.03010.0294
-1.9 0.02870.02810.02740.02680.02620.02560.02500.02440.02390.0233
-2.0 0.02280.02220.02170.02120.02070.02020.01970.01920.01880.0183

-2.1 0.01790.01740.01700.01660.01620.01580.01540.01500.01460.0143
-2.2 0.01390.01360.01320.01290.01250.01220.01190.01160.01130.0110
-2.3 0.01070.01040.01020.00990.00960.00940.00910.00890.00870.0084
-2.4 0.00820.00800.00780.00750.00730.00710.00690.00680.00660.0064
-2.5 0.00620.00600.00590.00570.00550.00540.00520.00510.00490.0048

-2.6 0.00470.00450.00440.00430.00410.00400.00390.00380.00370.0036
-2.7 0.00350.00340.00330.00320.00310.00300.00290.00280.00270.0026
-2.8 0.00260.00250.00240.00230.00230.00220.00210.00210.00200.0019
-2.9 0.00190.00180.00180.00170.00160.00160.00150.00150.00140.0014
-3.0 0.00130.00130.00130.00120.00120.00110.00110.00110.00100.0010

-3.1 0.00100.00090.00090.00090.00080.00080.00080.00080.00070.0007
-3.2 0.00070.00070.00060.00060.00060.00060.00060.00050.00050.0005
-3.3 0.00050.00050.00050.00040.00040.00040.00040.00040.00040.0003
-3.4 0.00030.00030.00030.00030.00030.00030.00030.00030.00030.0002
-3.5 0.00020.00020.00020.00020.00020.00020.00020.00020.00020.0002

## 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 < Ze then the null hypothesis H0 is accepted.
It states that there is no significance difference between Z-statistic & expected value of Z.

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