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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
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
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
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
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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