how to use the t table to solve statistics problems

Article Categories

Book categories, collections.

Academics & The Arts Articles
Math Articles
Statistics Articles

How to Use the T-table to Solve Statistics Problems

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

Sign up for the Dummies Beta Program to try Dummies' newest way to learn.

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

First, find the t-value for which you want the right-tail probability (call it t), and find the sample size (for example, n).
Next, find the row corresponding to the degrees of freedom (df) for your problem (for example, n – 1). Go across that row to find the two t-values between which your t falls. For example, if your t is 1.60 and your n is 7, you look in the row for df = 7 – 1 = 6. Across that row you find your t lies between t-values 1.44 and 1.94.
Then, go to the top of the columns containing the two t-values from Step 2. The right-tail (greater-than) probability for your t-value is somewhere between the two values at the top of these columns. For example, your t = 1.60 is between t-values 1.44 and 1.94 (df = 6); so the right tail probability for your t is between 0.10 (column heading for t = 1.44); and 0.05 (column heading for t = 1.94).

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:

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.

About This Article

This article is from the book:.

Statistics: 1001 Practice Problems For Dummies (+ Free Online Practice) ,

About the book author:

This article can be found in the category:.

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:

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:

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 .

Published by Zach

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.

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.

AP®︎/College Statistics

Unit 11: lesson 3.

Using a table to estimate P-value from t statistic

Want to join the conversation?

Video transcript

IMAGES

The t-table (for the t-distribution) is different from the Z-table (for the Z-distribution
8 Images Student T Distribution Table Two Tail And Description
T-test Table (One Tail & Two Tail)
Stats Introduction to the T Distribution
How to Use the t-Table to Solve Statistics Problems
How To Use A T Table

VIDEO

T distribution table, how to use t distribution table easy discussion
Mathematical Thinking vs Statistical Thinking
Sufficient Statistic
Limit theorem
What is Statistical Hypothesis Testing?
How many Musical Notes can you play?

COMMENTS

What Are the Six Steps of Problem Solving?
The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...
What Are the Components of a Statistical Table?
A statistical table contains several components designed to illustrate the data, including a title for the table, the table number, the heading and subheadings, the table body, the table spanner, dividers and table notes.
What Are Example Statistics and Probability Problems and Their Solutions?
Two examples of probability and statistics problems include finding the probability of outcomes from a single dice roll and the mean of outcomes from a series of dice rolls. The most-basic example of a simple probability problem is the clas...
How to Use the T-table to Solve Statistics Problems
How to use the t-table to find right-tail probabilities and p-values for hypothesis tests involving t: · Determine the confidence level you need
Student's t Table (Free Download)
How to use the t table · Step 1: Choose two-tailed or one-tailed · Step 2: Calculate the degrees of freedom · Step 3: Choose a significance level.
How to use the t-table
Using the T table · How To Know Which Statistical Test To Use For Hypothesis Testing · Student-t Distribution and Using the t-Chart · Find T Score(
Using the t Table to Find the P-value in One-Sample t Tests
I work through examples of finding the p-value for a one-sample t test using the t table. (It's impossible to find the exact p-value using
How to Read the t-Distribution Table
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
T Table: T Distribution Table With Usage Guide
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
T-Distribution Table of Critical Values
To calculate a two-sided confidence interval for a t-test, take the positive critical value from the t-distribution table and multiply it by your sample's
Using a table to estimate P-value from t statistic
In a significance test about a population mean, we first calculate a test statistic based on our sample results. We can then use a table to estimate the
T-Distribution Table (One Tail and Two-Tails)
T-Distribution Table (One Tail) ; ∞, ta = 1.282, 1.645, 1.960, 2.326 ; 1, 3.078, 6.314, 12.706, 31.821
T-Distribution / Student's T: Definition, Step by Step Articles, Video
Step 1: Subtract one from your sample size. This will be your degrees of freedom. Step 2: Look up the df in the left hand side of the t-distribution table.
How to Use the T-table to Solve Statistics Problems
... Statistics Problems - dummies. How exactly does a t-table differ from a z-table? Learn about all the important statistical differences here.