Calculating critical values of the student's-t distribution

Answer

T – Distribution Critical Values.

There are three different types of test namely,

1. Left tailed test

2. Right tailed test

3. Two-tailed tests

T Critical value determination for each test: -

1. Left tailed test

Step 1: Identify the level of significance always abbreviated as α.

Step 2: Determine the sample size, essential for the calculation of the degree of freedom.

Step 3: Calculate the degree of freedom abbreviated as df which is the sample size abbreviated as n minus 1.

Step 3 equation

$df=n-1$

Step 4: Use t distribution table

Step 5: Identify the degree of freedom column and match the degree of freedom with the level of significance in the one-tailed test option to get a critical value.

Step 6: From step 5 above critical value incorporate a negative sign. An indication of a left tailed test critical value.

NB: For a large sample size greater than 602, the t critical values are in the last column with the ∞ “infinite” symbol. Just incorporate a negative sign at the value obtained for the specific level of significance for a left-tailed test.

 2. Two tailed test

Step 1: Identify the level of significance always abbreviated as α.

Step 2: Determine the sample size, essential for the calculation of the degree of freedom.

Step 3: Calculate the degree of freedom abbreviated as df which is the sample size abbreviated as n minus 1.

Step 3 equation

$df=n-1$

Part 1

Step 4: Since it is a two-tailed test and t distribution is symmetrical, divide the level of significance by 2.

Step 4 equation

$\frac{\alpha }{2}$

Step 5: Use t distribution table

Step 6: Identify the degree of freedom column and match the degree of freedom with the level of significance in the one-tailed test option to get critical value.

Step 7: From step 6 above critical value incorporate a negative and positive sign. An indication of a two-tailed test critical values.

Part 2: Alternative

Step 4: Use t distribution table

Step 5: Identify the degree of freedom column and match the degree of freedom with the level of significance in the two-tailed test option to get critical value.

Step 6: From step 5 above critical value incorporate a negative and positive sign. An indication of a two-tailed test critical values.

NB: For large sample size greater than 602, the t critical values are in the last column with the ∞ “infinite” symbol. Just incorporate a negative sign and a positive sign at the value obtained for a specific level of significance for a two-tailed test.

3. Right tailed test

Step 1: Identify the level of significance always abbreviated as α.

Step 2: Determine the sample size, essential for the calculation of the degree of freedom.

Step 3: Calculate the degree of freedom abbreviated as df which is the sample size abbreviated as n minus 1.

Step 3 equation

$df=n-1$

Step 4: Use t distribution table

Step 5: Identify the degree of freedom column and match the degree of freedom with the level of significance in the one-tailed test option to get a critical valu.

Step 6: The positive the value obtained from the above step is the critical value of a right-tailed test.

NB: For large sample size greater than 602, the t critical values are in the last column with the ∞ “infinite” symbol. Just incorporate a positive sign at the value obtained for a specific level of significance for a right tailed test.

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