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How to Use the T-table to Solve Statistics Problems

Statistics: 1001 practice problems for dummies (+ free online practice).

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How to use the t-table to find right-tail probabilities and p-values for hypothesis tests involving t:.

The row near the bottom with Z in the df column gives right-tail (greater-than) probabilities from the Z-distribution.

Use the t table to find t*-values (critical values) for a confidence interval involving t:

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Practice solving problems using the t-table sample questions below

For a study involving one population and a sample size of 18 (assuming you have a t-distribution), what row of the t-table will you use to find the right-tail (“greater than”) probability affiliated with the study results?

Answer: df = 17

The study involving one population and a sample size of 18 has n – 1 = 18 – 1 = 17 degrees of freedom.

For a study involving a paired design with a total of 44 observations, with the results assuming a t - distribution, what row of the table will you use to find the probability affiliated with the study results?

Answer: df = 21

A matched-pairs design with 44 total observations has 22 pairs. The degrees of freedom is one less than the number of pairs: n – 1 = 22 – 1 = 21.

A t- value of 2.35, from a t- distribution with 14 degrees of freedom, has an upper-tail (“greater than”) probability between which two values on the t-table?

Answer: 0.025 and 0.01

Using the t-table, locate the row with 14 degrees of freedom and look for 2.35. However, this exact value doesn’t lie in this row, so look for the values on either side of it: 2.14479 and 2.62449. The upper-tail probabilities appear in the column headings; the column heading for 2.14479 is 0.025, and the column heading for 2.62449 is 0.01.

Hence, the upper-tail probability for a t- value of 2.35 must lie between 0.025 and 0.01.

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Statology

Statistics Made Easy

How to Read the t-Distribution Table

This tutorial explains how to read and interpret the t-Distribution table .

What is the t-Distribution Table?

The t-distribution table  is a table that shows the critical values of the t distribution. To use the t-distribution table, you only need to know three values:

Here is an example of the t-Distribution table, with the degrees of freedom listed along the left side of the table and the alpha levels listed along the top of the table:

t-Distribution table in statistics

When you conduct a t-test, you can compare the test statistic from the t-test to the critical value from the t-Distribution table. If the test statistic is greater than the critical value found in the table, then you can reject the null hypothesis of the t-test and conclude that the results of the test are statistically significant.

Let’s walk through some examples of how to use the t-Distribution table.

Examples of How to Use the t-Distribution Table

The following examples explain how to use the t-Distribution table in several different scenarios.

Example #1: One-tailed t-test for a mean

A researcher recruits 20 subjects for a study and conducts a one-tailed t-test for a mean using an alpha level of 0.05.

Question: Once she conducts her one-tailed t-test and obtains a test statistic t , what critical value should she compare  t  to?

Answer: For a t-test with one sample, the degrees of freedom is equal to  n-1 , which is 20-1 = 19 in this case. The problem also tells us that she is conducting a one-tailed test and that she is using an alpha level of 0.05, so the corresponding critical value in the t-distribution table is  1.729 .

Example #2: Two-tailed t-test for a mean

A researcher recruits 18 subjects for a study and conducts a two-tailed t-test for a mean using an alpha level of 0.10.

Question: Once she conducts her two-tailed t-test and obtains a test statistic t , what critical value should she compare  t  to?

Answer: For a t-test with one sample, the degrees of freedom is equal to  n-1 , which is 18-1 = 17 in this case. The problem also tells us that she is conducting a two-tailed test and that she is using an alpha level of 0.10, so the corresponding critical value in the t-distribution table is  1.74 .

Example #3: Determining the critical value

A researcher conducts a two-tailed t-test for a mean using a sample size of 14 and an alpha level of 0.05. 

Question: What would the absolute value of her test statistic  t  need to be in order for her to reject the null hypothesis?

Answer: For a t-test with one sample, the degrees of freedom is equal to  n-1 , which is 14-1 = 13 in this case. The problem also tells us that she is conducting a two-tailed test and that she is using an alpha level of 0.05, so the corresponding critical value in the t-distribution table is  2.16 . This means that she can reject the null hypothesis if the test statistic  t  is less than -2.16 or greater than 2.16.

Example #4: Comparing a critical value to a test statistic

A researcher conducts a right-tailed t-test for a mean using a sample size of 19 and an alpha level of 0.10.

Question: The test statistic t  turns out to be 1.48. Can she reject the null hypothesis?

Answer: For a t-test with one sample, the degrees of freedom is equal to  n-1 , which is 19-1 = 18 in this case. The problem also tells us that she is conducting a right-tailed test (which is a one-tailed test) and that she is using an alpha level of 0.10, so the corresponding critical value in the t-distribution table is  1.33 . Since her test statistic  t  is greater than 1.33, she can reject the null hypothesis.

Should You Use the t Table or the z Table?

One problem that students frequently encounter is determining if they should use the t-distribution table or the z table to find the critical values for a particular problem. If you’re stuck on this decision, you can u se the following flow chart to determine which table you should use:

Z table vs. t table

Additional Resources

For a complete list of critical value tables, including a binomial distribution table, a chi-square distribution table, a z-table, and more, check out this page .

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t Table: t Distribution Table with Usage Guide

The t table or t distribution table is used in statistics when the standard deviation (σ) of a population is not known and the sample size is small, that is, n<30.

The t table is a table that shows the critical values of the t distribution and is given below:

t-Table: t-Distribution Table with Usage Guide

How to use the t Table or t Distribution Table?

Using the t table is fairly simple during a t-test since you only need to know three values:

In the t-table, the first column denotes the degrees of freedom of the t-test. So, when you conduct a t-test, you can compare the test statistic from the t-test to the critical value from the t table or t distribution table.

If the test statistic is greater than the critical value found in the table, then you can reject the null hypothesis of the t-test and conclude that the results of the test are statistically significant.

You can learn more about how to use the t table to solve statistics problems in this article by Dummies.

What is the t-distribution?

The t-distribution or student’s t-distribution is a type of normal distribution that is used for smaller sample sizes where there are more observations towards the mean and fewer observations in the tails.

What is the t-distribution? - t-Table: t-Distribution Table

This means the t-distribution forms a bell curve when plotted on a graph. It is used to find the corresponding p-value from a statistical test that uses the t-distribution such as t-tests and regression analysis.

When do you use the t table and the z table?

Both t table and z table are used when the population standard deviation is unknown. However, if the sample size is less than 30 then the t table should be used and if not, the z table should be used.

The z table is given below:

When do you use the t table vs the z table

That is it for this article. If you are still confused about how to use the t table, please let us know in the comments.

t Table: t Distribution Table with Usage Guide

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AP®︎/College Statistics

Unit 11: lesson 3.

Using a table to estimate P-value from t statistic

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Video transcript

IMAGES

  1. The t-table (for the t-distribution) is different from the Z-table (for the Z-distribution

    how to use the t table to solve statistics problems

  2. 8 Images Student T Distribution Table Two Tail And Description

    how to use the t table to solve statistics problems

  3. T-test Table (One Tail & Two Tail)

    how to use the t table to solve statistics problems

  4. Stats Introduction to the T Distribution

    how to use the t table to solve statistics problems

  5. How to Use the t-Table to Solve Statistics Problems

    how to use the t table to solve statistics problems

  6. How To Use A T Table

    how to use the t table to solve statistics problems

VIDEO

  1. T distribution table, how to use t distribution table easy discussion

  2. Mathematical Thinking vs Statistical Thinking

  3. Sufficient Statistic

  4. Limit theorem

  5. What is Statistical Hypothesis Testing?

  6. How many Musical Notes can you play?

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