T Critical Value Calculator + Online Solver With Free Steps

The T Critical Value Calculator is a free online statistics tool for computing the T value for one-tailed and two-tailed probability.

Additionally, the student t distribution table’s mapped t-value is displayed by the critical values calculator as well.

What Is a T Critical Value Calculator?

The T Critical Value Calculator is an online tool that calculates the T distribution cut-off point. It closely resembles the Z critical value.

The only significant variation is that the cutoff parameters for the t distribution and normal distribution have slightly varying values, respectively.

T value determines how much of a difference there is in comparison to the variation in the sampled data. It is simply the calculated variation stated in conventional error units.

A considerable difference is demonstrated if the t value is higher. There is a possibility of no substantial variation if the t-value is equal to 0.

A critical value calculator determines the t distribution’s critical values based on the probability of 2 alpha values as well as the DOF (Degree of Freedom). A hypothetical probability distribution that mimics a standard distribution is referred to as a “T-Distribution table.“

The closer a distribution resembles a conventional normal distribution with a mean of 0 and a standard deviation of 1 depending on the total number of DOFs. It resembles the conventional normal curve which is uniform, bell-shaped, and linear.

A degree of freedom (DOF) and importance level of alpha is applied to compute the T’s Critical value by using a T critical value calculator. In this article, we’ll go over how to determine the t critical value using both the Formula for the alpha calculation and the t distribution table.

How To Use a T Critical Value Calculator?

You can use the T Critical Value Calculator by following the detailed instructions below. The calculator will provide you with the desired results in a few seconds. You can therefore easily use the calculator to get the T Critical Value for the given data points.

Step 1

Fill in the provided input boxes with the Degrees of Freedom, Level of Significance, Total number of tails, and the direction.

Step 2

To calculate the T Critical Value for the provided data and to view the complete, step-by-step solution for the T Critical Value Calculation, click the “Submit” button.

How Does a T Critical Value Calculator Work?

The T Critical Value Calculator works by calculating the Alpha Value before computing the critical Probability.

Use this formula to determine the alpha value:

value of alpha = 1 – ( $ \frac{confidence \; level}{100} $)

The degree of confidence indicates how likely it is that a statistical parameter also applies to the population being studied. Typically, a percentage is used to represent this figure.

A 95 percent degree of confidence within a sample group, for instance, denotes that there is a 95 percent likelihood that the given criteria will hold for the full population.

You would use the given calculation to ascertain the alpha value with an 85% level of confidence.

Alpha = 1 – ( $ \frac{85}{100} $) = 1 – (0.85) = 0.15

It comes to 0.15. This example’s alpha value is 0.15.

T Table

The freedom degrees (DOF) in a T distribution are different from those in a standard distribution.

A distribution that is utilized to evaluate an overall mean hypothesis when the overall standard deviation is unknown, the sampling size is small, and the sampling means are expected to have a standard distribution.

To calculate the value of T using the t table, just use the aforementioned t critical value table.

Solved Examples

Let’s solve some examples to better understand the working of the T Critical Value Calculator.

Example 1

For a significance level of 5% and 30 degrees of freedom, determine the crucial t value (one tail and two tails).

Solution

First, determine the values.

Level of significance = 5% = $ \frac{5}{100} $ = 0.05

30 degrees of freedom.

Secondly, Locate the degree of freedom (DOF) and significance level in the top row and left side, respectively, of the t distribution table below. Obtain the relevant value from the table.

T’s one-tailed critical value is 1.6978.

Repeat step 1 and use the two-tailed t table below for two-tailed probability in step 3.

T critical value = 2.0428

Example 2

Locate the essentials

Without utilizing a t & z value calculator, let’s determine the value of t.

Solution

To compute the t value using the t value table, follow these steps:

Determine the sample size in the first step. Consider there to be 5 samples.

n = 5

Calculate the degrees of freedom (DOFs) in step two. Add 1 less to the sample size.

df = n – 5 = 5 – 1 = 4

Determine the alpha level’s value in step three. Take 0.05 as the value for the time being.

α = 0.05

In step 4 Look up the values of df and its related alpha level in the list below. As a result, we will have:

t = 2.015 

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