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Well, finding critical values becomes easy with the ease of our critical value calculator; this efficient tool allows you to calculate critical values for the t and z distributions. A t critical value is the ‘cut-off point’ on a t distribution. No doubt, the t value is almost the same with the z critical value that is said to be as the ‘cut-off point’ on a normal distribution. When it comes to variation between these two, they have different shapes.

However, the values for their cut-off points vary slightly too. When conducting a hypothesis test, you can use the t value to compare against a t score that you’ve determined. The easiest way to get the t value is by using the above t value calculator, and for z value, you can use the z critical value calculator.

A critical value is said to be as a line on a graph that divides a distribution graph into sections that indicate ‘rejection regions.’ Generally, if a test value falls into a rejection rejoin, then it means that an accepted hypothesis (represent as a null hypothesis) should be rejected. And, if the test value falls into the accepted range, then remember that the null hypothesis cannot be rejected. You can readily find critical value using simple critical value formula and a critical value table. However, our remarkable and tested critical number calculator helps to understand how to calculate critical value.

Two formulas are taken into account to attain critical value, these are:

- Critical Value = Margin of Error/Standard Deviation of the Statistic
- Critical Value = Margin of Error/Standard Error of the Statistic

Keep in mind; if the sampling distribution of the statistic is normal or nearly normal, then the critical value can be stated as a ‘t score’ or as a ‘z score.’

Finding critical values becomes easy with the following steps:

α = 1 – (confidence level / 100)

(p*): p* = 1 – α/2

- If you want to express the critical value as a z-score, then you ought to find the z-score having a cumulative probability equal to the critical probability (p*). Also, you can use the above accurate, critical value z calculator to get z value

- First, you have to figure out the degree of freedom (df). Typically, (df) is equal to the sample size minus(-) one (1)
- The (t*) is said to be as the t statistic that having a cumulative probability equal to the critical probability (p*) and degrees of freedom equal to (df) and a). Simply enter the values into the designated field of the above fastest critical t value calculator to get t value

No doubt, there is different critical values calculator that often utilized by folks, but we are provided simple but highly accurate critical value calculator that allows you to calculate t critical value and z critical value for any tail. In straight forward words, you can take this tool into account to get an idea about the critical value statistics for t & z values. The tool works as natural assistance to know how to find critical value of t & z.

Simply, you just have to follow the given steps:

- First of all, you have to select one option from the drop-down, it can be either ‘Critical Value For T’ or ‘Critical Value For Z.’
- If you select a critical value for T, then you have to enter the value of significance level and degree of freedom into the designated field and hit the calculate button to attain T value
- If you select a critical value for Z, then you just have to enter the value of significance level and hit the calculate of this tool to attain Z value

**Note:** Remember that critical values can take into account for a two-tailed test or one-tailed (right-tailed or left-tailed. It all based on the data, statisticians determine which test to perform first. You can get the assistance of calculating t and z value of Left Tail and Right Tail with this left and right critical value calculator.

You can readily take a look at a critical value if you have a left tailed test or right-tailed test (or potentially both).

Let’s find a critical value for a 90% confidence level (two-tailed test):

- First, you have to subtract the confidence level from 100% to figure out the α level: 100% – 90% = 10%
- Right after, you have to convert step 1 to a decimal: 10% = 0.10
- Then, you have to divide step 2 by 2 (this is known as ‘α/2’), means 0.10 = 0.05, this is said to be as the area in each tail
- Then, you have to subtract step 3 from 1 as we need the area in the middle, not the area in the tail, so, 1 – 0.05 = .95
- Once done, take a look at the area from step in the z critical value table. The area that is at z = 1.645 is your critical value for a confidence level of 90%.

Well, there is no need to perform the above calculations every time; here we are going to list some confidence levels and their critical values that might work for you!

Confidence Level |
Critical Value (Z-score) |

0.90 | 1.645 |

0.91 | 1.70 |

0.92 | 1.75 |

0.93 | 1.81 |

0.94 | 1.88 |

0.95 | 1.96 |

0.96 | 2.05 |

0.97 | 2.17 |

0.98 | 2.33 |

0.99 | 2.575 |

Let’s find the critical value for an alpha of .05

- First of all, you ought to subtract alpha from 1 that is 1 – .05 = .95
- Then, you ought to divide step 1 by 2 as we are looking for a two-tailed test that is .95 / 2 = .475
- Very next, take a look at z-table and find the answer from step 2 in the middle section of the z-table
- In this example, you should have to found the number .4750. Take a look at the z table; you will see the number 1.9 to the far left, then look at the top of the column, you will see .06. Add both of them together to attain 1.96, that’s the critical value

Let’s find the critical value in the z-table for an alpha, α level of 0.0079.

- Draw a simple diagram and shade the area in the right tail as that helps you to visualize which area you’re looking for
- Then, you ought to subtract (α) from 0.5 that is 0.5-0.0079 = 0.4921
- Right after, find the result from step 2 in the center of the table z, the near area to 0.4921 is 0.4922 at z=2.42

Note: The value appears twice in the table-z as we are looking for both left & right tail, so don’t forget to add the plus (+) or minus (-) sign! In this example, we get ±1.96

Let’s find the value in the z-table for α=.012 (left-tailed test)

- Draw a diagram and shade the area in the left-tail as you are going to perform left-test, this is the area that indicates alpha, α
- In this step, you have to subtract alpha (α) from 0.5 that is 0.5 – 0.012 = 0.488
- Then, you ought to figure out the result from step 2 in the center part of the table-z
- Once done, then you ought to add a negative (-) sigh to step 3 as left-tail critical values are always negative (-) that is -2.26

Critical values are the values that are used in statistics for hypothesis testing. No doubt, when you work with statistics, you people are working with a small percentage (a sample) of a population.

You might have statistics for voting habits from 5% of students and 2% of democratic voters and their results. As you are just working with a fraction of the population and not with the entire population, that’s the reason why you can never be 100 percent certain that your outcomes reflect the actual population’s outcomes. You might be 90% or even 99% certain about the outcomes, but you can never be 100%. So, hypothesis testing will be taken into account to know how accurate your outcomes are.

Sometimes people want to know the area between the mean and some positive value, that’s where they will use the right-hand z critical value table. But other times they might want to know the area in a left-tail, in such case these people use the left-hand z-table.

The z-table is the normal distribution shows the area to the right-hand side of the curve. You can use these values to determine the area between z=0 and any positive (+) value.

z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
---|---|---|---|---|---|---|---|---|---|---|

0.0 | 0.0000 | 0.0040 | 0.0080 | 0.0120 | 0.0160 | 0.0199 | 0.0239 | 0.0279 | 0.0319 | 0.0359 |

0.1 | 0.0398 | 0.0438 | 0.0478 | 0.0517 | 0.0557 | 0.0596 | 0.0636 | 0.0675 | 0.0714 | 0.0753 |

0.2 | 0.0793 | 0.0832 | 0.0871 | 0.0910 | 0.0948 | 0.0987 | 0.1026 | 0.1064 | 0.1103 | 0.1141 |

0.3 | 0.1179 | 0.1217 | 0.1255 | 0.1293 | 0.1331 | 0.1368 | 0.1406 | 0.1443 | 0.1480 | 0.1517 |

0.4 | 0.1554 | 0.1591 | 0.1628 | 0.1664 | 0.1700 | 0.1736 | 0.1772 | 0.1808 | 0.1844 | 0.1879 |

0.5 | 0.1915 | 0.1950 | 0.1985 | 0.2019 | 0.2054 | 0.2088 | 0.2123 | 0.2157 | 0.2190 | 0.2224 |

0.6 | 0.2257 | 0.2291 | 0.2324 | 0.2357 | 0.2389 | 0.2422 | 0.2454 | 0.2486 | 0.2517 | 0.2549 |

0.7 | 0.2580 | 0.2611 | 0.2642 | 0.2673 | 0.2704 | 0.2734 | 0.2764 | 0.2794 | 0.2823 | 0.2852 |

0.8 | 0.2881 | 0.2910 | 0.2939 | 0.2967 | 0.2995 | 0.3023 | 0.3051 | 0.3078 | 0.3106 | 0.3133 |

0.9 | 0.3159 | 0.3186 | 0.3212 | 0.3238 | 0.3264 | 0.3289 | 0.3315 | 0.3340 | 0.3365 | 0.3389 |

1.0 | 0.3413 | 0.3438 | 0.3461 | 0.3485 | 0.3508 | 0.3531 | 0.3554 | 0.3577 | 0.3599 | 0.3621 |

1.1 | 0.3643 | 0.3665 | 0.3686 | 0.3708 | 0.3729 | 0.3749 | 0.3770 | 0.3790 | 0.3810 | 0.3830 |

1.2 | 0.3849 | 0.3869 | 0.3888 | 0.3907 | 0.3925 | 0.3944 | 0.3962 | 0.3980 | 0.3997 | 0.4015 |

1.3 | 0.4032 | 0.4049 | 0.4066 | 0.4082 | 0.4099 | 0.4115 | 0.4131 | 0.4147 | 0.4162 | 0.4177 |

1.4 | 0.4192 | 0.4207 | 0.4222 | 0.4236 | 0.4251 | 0.4265 | 0.4279 | 0.4292 | 0.4306 | 0.4319 |

1.5 | 0.4332 | 0.4345 | 0.4357 | 0.4370 | 0.4382 | 0.4394 | 0.4406 | 0.4418 | 0.4429 | 0.4441 |

1.6 | 0.4452 | 0.4463 | 0.4474 | 0.4484 | 0.4495 | 0.4505 | 0.4515 | 0.4525 | 0.4535 | 0.4545 |

1.7 | 0.4554 | 0.4564 | 0.4573 | 0.4582 | 0.4591 | 0.4599 | 0.4608 | 0.4616 | 0.4625 | 0.4633 |

1.8 | 0.4641 | 0.4649 | 0.4656 | 0.4664 | 0.4671 | 0.4678 | 0.4686 | 0.4693 | 0.4699 | 0.4706 |

1.9 | 0.4713 | 0.4719 | 0.4726 | 0.4732 | 0.4738 | 0.4744 | 0.4750 | 0.4756 | 0.4761 | 0.4767 |

2.0 | 0.4772 | 0.4778 | 0.4783 | 0.4788 | 0.4793 | 0.4798 | 0.4803 | 0.4808 | 0.4812 | 0.4817 |

2.1 | 0.4821 | 0.4826 | 0.4830 | 0.4834 | 0.4838 | 0.4842 | 0.4846 | 0.4850 | 0.4854 | 0.4857 |

2.2 | 0.4861 | 0.4864 | 0.4868 | 0.4871 | 0.4875 | 0.4878 | 0.4881 | 0.4884 | 0.4887 | 0.4890 |

2.3 | 0.4893 | 0.4896 | 0.4898 | 0.4901 | 0.4904 | 0.4906 | 0.4909 | 0.4911 | 0.4913 | 0.4916 |

2.4 | 0.4918 | 0.4920 | 0.4922 | 0.4925 | 0.4927 | 0.4929 | 0.4931 | 0.4932 | 0.4934 | 0.4936 |

2.5 | 0.4938 | 0.4940 | 0.4941 | 0.4943 | 0.4945 | 0.4946 | 0.4948 | 0.4949 | 0.4951 | 0.4952 |

2.6 | 0.4953 | 0.4955 | 0.4956 | 0.4957 | 0.4959 | 0.4960 | 0.4961 | 0.4962 | 0.4963 | 0.4964 |

2.7 | 0.4965 | 0.4966 | 0.4967 | 0.4968 | 0.4969 | 0.4970 | 0.4971 | 0.4972 | 0.4973 | 0.4974 |

2.8 | 0.4974 | 0.4975 | 0.4976 | 0.4977 | 0.4977 | 0.4978 | 0.4979 | 0.4979 | 0.4980 | 0.4981 |

2.9 | 0.4981 | 0.4982 | 0.4982 | 0.4983 | 0.4984 | 0.4984 | 0.4985 | 0.4985 | 0.4986 | 0.4986 |

3.0 | 0.4987 | 0.4987 | 0.4987 | 0.4988 | 0.4988 | 0.4989 | 0.4989 | 0.4989 | 0.4990 | 0.4990 |

3.1 | 0.4990 | 0.4991 | 0.4991 | 0.4991 | 0.4992 | 0.4992 | 0.4992 | 0.4992 | 0.4993 | 0.4993 |

3.2 | 0.4993 | 0.4993 | 0.4994 | 0.4994 | 0.4994 | 0.4994 | 0.4994 | 0.4995 | 0.4995 | 0.4995 |

3.3 | 0.4995 | 0.4995 | 0.4995 | 0.4996 | 0.4996 | 0.4996 | 0.4996 | 0.4996 | 0.4996 | 0.4997 |

3.4 | 0.4997 | 0.4997 | 0.4997 | 0.4997 | 0.4997 | 0.4997 | 0.4997 | 0.4997 | 0.4997 | 0.4998 |

3.5 | 0.4998 | 0.4998 | 0.4998 | 0.4998 | 0.4998 | 0.4998 | 0.4998 | 0.4998 | 0.4998 | 0.4998 |

3.6 | 0.4998 | 0.4998 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 |

3.7 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 |

3.8 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 | 0.4999 |

The left z-table shows the area to the left of Z.

Z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
---|---|---|---|---|---|---|---|---|---|---|

0.0 | 0.5000 | 0.5040 | 0.5080 | 0.0120 | 0.0160 | 0.0199 | 0.5239 | 0.0279 | 0.0319 | 0.0359 |

0.1 | 0.5398 | 0.5438 | 0.5478 | 0.5517 | 0.5557 | 0.5596 | 0.5636 | 0.5675 | 0.5714 | 0.5753 |

0.2 | 0.5793 | 0.5832 | 0.5871 | 0.5910 | 0.5948 | 0.5987 | 0.6064 | 0.1064 | 0.6103 | 0.6141 |

0.3 | 0.6179 | 0.6217 | 0.6255 | 0.6293 | 0.6331 | 0.6368 | 0.6406 | 0.6443 | 0.6480 | 0.6517 |

0.4 | 0.6554 | 0.6591 | 0.6628 | 0.6664 | 0.6700 | 0.6736 | 0.6772 | 0.6808 | 0.6844 | 0.6879 |

0.5 | 0.6915 | 0.6950 | 0.6985 | 0.7019 | 0.7054 | 0.7088 | 0.7123 | 0.7157 | 0.7190 | 0.7224 |

0.6 | 0.7257 | 0.7291 | 0.7324 | 0.7357 | 0.7389 | 0.7422 | 0.7454 | 0.7486 | 0.7517 | 0.7549 |

0.7 | 0.7580 | 0.7611 | 0.7642 | 0.7673 | 0.7704 | 0.7734 | 0.7764 | 0.7794 | 0.7823 | 0.7852 |

0.8 | 0.7881 | 0.7910 | 0.7939 | 0.7967 | 0.7995 | 0.8023 | 0.8051 | 0.8078 | 0.8106 | 0.8133 |

0.9 | 0.8159 | 0.8186 | 0.8212 | 0.8238 | 0.8264 | 0.8289 | 0.8315 | 0.8340 | 0.8365 | 0.8389 |

1.0 | 0.8413 | 0.8438 | 0.8461 | 0.8485 | 0.8508 | 0.8531 | 0.8554 | 0.8577 | 0.8599 | 0.8621 |

1.1 | 0.8643 | 0.8665 | 0.8686 | 0.8708 | 0.8729 | 0.8749 | 0.8770 | 0.8790 | 0.8810 | 0.8830 |

1.2 | 0.8849 | 0.8869 | 0.8888 | 0.8907 | 0.8925 | 0.8944 | 0.8962 | 0.8980 | 0.8997 | 0.9015 |

1.3 | 0.9032 | 0.9049 | 0.9066 | 0.9082 | 0.9099 | 0.9115 | 0.9131 | 0.9147 | 0.9162 | 0.9177 |

1.4 | 0.9192 | 0.9207 | 0.9222 | 0.9236 | 0.9251 | 0.9265 | 0.9279 | 0.9292 | 0.9306 | 0.9319 |

1.5 | 0.9332 | 0.9345 | 0.9357 | 0.9370 | 0.9382 | 0.9394 | 0.9406 | 0.9418 | 0.9429 | 0.9441 |

1.6 | 0.9452 | 0.9463 | 0.9474 | 0.9484 | 0.9495 | 0.9505 | 0.9515 | 0.9525 | 0.9535 | 0.9545 |

1.7 | 0.9554 | 0.9564 | 0.9573 | 0.9582 | 0.9591 | 0.9599 | 0.9608 | 0.9616 | 0.9625 | 0.9633 |

1.8 | 0.9641 | 0.9649 | 0.9656 | 0.9664 | 0.9671 | 0.9678 | 0.9686 | 0.9693 | 0.9699 | 0.9706 |

1.9 | 0.9713 | 0.9719 | 0.9726 | 0.9732 | 0.9738 | 0.9744 | 0.9750 | 0.9756 | 0.9761 | 0.9767 |

2.0 | 0.9772 | 0.9778 | 0.9783 | 0.9788 | 0.9793 | 0.9798 | 0.9803 | 0.9808 | 0.9812 | 0.9817 |

2.1 | 0.9821 | 0.9826 | 0.9830 | 0.9834 | 0.9838 | 0.9842 | 0.9846 | 0.9850 | 0.9854 | 0.9857 |

2.2 | 0.9861 | 0.9864 | 0.9868 | 0.9871 | 0.9875 | 0.9878 | 0.9881 | 0.9884 | 0.9887 | 0.9890 |

2.3 | 0.9893 | 0.9896 | 0.9898 | 0.9901 | 0.9904 | 0.9906 | 0.9909 | 0.9911 | 0.9913 | 0.9916 |

2.4 | 0.9918 | 0.9920 | 0.9922 | 0.9925 | 0.9927 | 0.9929 | 0.9931 | 0.9932 | 0.9934 | 0.9936 |

2.5 | 0.9938 | 0.9940 | 0.9941 | 0.9943 | 0.9945 | 0.9946 | 0.9948 | 0.9949 | 0.9951 | 0.9952 |

2.6 | 0.9953 | 0.9955 | 0.9956 | 0.9957 | 0.9959 | 0.9960 | 0.9961 | 0.9962 | 0.9963 | 0.9964 |

2.7 | 0.9965 | 0.9966 | 0.9967 | 0.9968 | 0.9969 | 0.9970 | 0.9971 | 0.9972 | 0.9973 | 0.9974 |

2.8 | 0.9974 | 0.9975 | 0.9976 | 0.9977 | 0.9977 | 0.9978 | 0.9979 | 0.9979 | 0.9980 | 0.9981 |

2.9 | 0.9981 | 0.9982 | 0.9982 | 0.9983 | 0.9984 | 0.9984 | 0.9985 | 0.9985 | 0.9986 | 0.9986 |

3.0 | 0.9987 | 0.9987 | 0.9987 | 0.9988 | 0.9988 | 0.9989 | 0.9989 | 0.9989 | 0.9990 | 0.9990 |

df | a = 0.1 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 | 0.0005 |
---|---|---|---|---|---|---|---|

∞ | t_{a} = 1.282 |
1.645 | 1.960 | 2.326 | 2.576 | 3.091 | 3.291 |

1 | 3.078 | 6.314 | 12.706 | 31.821 | 63.656 | 318.289 | 636.578 |

2 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | 22.328 | 31.600 |

3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 10.214 | 12.924 |

4 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | 7.173 | 8.610 |

5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | 5.894 | 6.869 |

6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | 5.208 | 5.959 |

7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | 4.785 | 5.408 |

8 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 | 4.501 | 5.041 |

9 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 | 4.297 | 4.781 |

10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 4.144 | 4.587 |

11 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 | 4.025 | 4.437 |

12 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 | 3.930 | 4.318 |

13 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 | 3.852 | 4.221 |

14 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 | 3.787 | 4.140 |

15 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 | 3.733 | 4.073 |

16 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 | 3.686 | 4.015 |

17 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 | 3.646 | 3.965 |

18 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 | 3.610 | 3.922 |

19 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 | 3.579 | 3.883 |

20 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 | 3.552 | 3.850 |

21 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 | 3.527 | 3.819 |

22 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 | 3.505 | 3.792 |

23 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 | 3.485 | 3.768 |

24 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 | 3.467 | 3.745 |

25 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 | 3.450 | 3.725 |

26 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 | 3.435 | 3.707 |

27 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 | 3.421 | 3.689 |

28 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 | 3.408 | 3.674 |

29 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 | 3.396 | 3.660 |

30 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 | 3.385 | 3.646 |

60 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 | 3.232 | 3.460 |

120 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 | 3.160 | 3.373 |

1000 | 1.282 | 1.646 | 1.962 | 2.330 | 2.581 | 3.098 | 3.300 |

df | a = 0.2 | 0.10 | 0.05 | 0.02 | 0.01 | 0.002 | 0.001 |
---|---|---|---|---|---|---|---|

∞ | t_{a} = 1.282 |
1.645 | 1.960 | 2.326 | 2.576 | 3.091 | 3.291 |

1 | 3.078 | 6.314 | 12.706 | 31.821 | 63.656 | 318.289 | 636.578 |

2 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | 22.328 | 31.600 |

3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 10.214 | 12.924 |

4 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | 7.173 | 8.610 |

5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | 5.894 | 6.869 |

6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | 5.208 | 5.959 |

7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | 4.785 | 5.408 |

8 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 | 4.501 | 5.041 |

9 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 | 4.297 | 4.781 |

10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 4.144 | 4.587 |

11 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 | 4.025 | 4.437 |

12 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 | 3.930 | 4.318 |

13 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 | 3.852 | 4.221 |

14 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 | 3.787 | 4.140 |

15 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 | 3.733 | 4.073 |

16 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 | 3.686 | 4.015 |

17 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 | 3.646 | 3.965 |

18 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 | 3.610 | 3.922 |

19 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 | 3.579 | 3.883 |

20 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 | 3.552 | 3.850 |

21 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 | 3.527 | 3.819 |

22 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 | 3.505 | 3.792 |

23 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 | 3.485 | 3.768 |

24 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 | 3.467 | 3.745 |

25 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 | 3.450 | 3.725 |

26 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 | 3.435 | 3.707 |

27 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 | 3.421 | 3.689 |

28 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 | 3.408 | 3.674 |

29 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 | 3.396 | 3.660 |

30 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 | 3.385 | 3.646 |

60 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 | 3.232 | 3.460 |

120 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 | 3.160 | 3.373 |

8 | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 | 3.091 | 3.291 |

The formula for calculating a z-score is:

**z = (X – μ) / σ**

Where;

- X is the value of the element
- μ is the population mean
- σ is the standard deviation

**For example:**

If you have a test score of 85, a mean (μ) of 45 and a standard deviation (σ) of 23, then what’s your z-score?

X = 85, μ = 45, σ = 23

z = (85 – 45) / 23; = 40 / 23

z = 1.7391

It means, you z-score are 1.7391 standard deviations above the mean.

In simple words, a sample means with a z-score greater than or equal to the critical value of 1.645 is said to be as significant at the 0.05 level.

The z*– value 1.96 for a 95 confidence interval, also you can see some common confidence levels and their critical values in the above table.

The critical z value is a term that linked to the area under the standard normal model. And, this z value is sometimes written as **z**_{a}, where the alpha level, a, is said to be as the area in the tail.

For example:

**Z**_{10 = }1.28

Remember that, z-score is used when the sampling distribution is normal or close to normal.

The degrees of freedom (df) are said to be as the amount of information of your data provide that you can spend to determine the values of unknown population parameters, and find out the variability of these estimates. You can enter (df) and significance level into the above critical value calculator t, to get your t value.

The standard formula for calculating t-score is:

**t = [ x – μ ] / [ s / sqrt( n ) ]**

Where,

• x is the sample mean

• μ is the population mean

• s is the sample’s standard deviation

• n is the sample size

Then, you have to account for the (df) degrees of freedom that is the sample size minus (-) 1, means (df) =n – 1. Also, you can get the ease of calculating t-value with our t value calculator.

You can readily determine a confidence level for a data set by taking half of the size of the confidence interval; you just have to multiply it by the square root of the sample size, and then dividing by the sample standard deviation. Take a look at the resulting z or t score in a table to find the level.

When it comes to hypothesis testing, a critical value is a point on the test distribution that is taken into account to compare the test statistic to figure out whether to reject the null hypothesis. If the absolute value of the test statistic is greater than the value, then you can declare the statistical significance and reject the null hypothesis.

Finding critical values are immensely important for statistical testing data and even it is the main factors in hypothesis testing that can help to validate or disprove commonly accepted information. So, bookmark us and feel free to use our free statistics tools.