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**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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