How To Use Student T Distribution Table? Fast Answers

The Student T distribution table, also known as the T distribution table or T table, is a statistical tool used to determine the critical values of the T statistic. It is commonly used in hypothesis testing and confidence interval construction. In this article, we will explore how to use the Student T distribution table to obtain fast answers for various statistical problems.

Understanding the Student T Distribution Table

The Student T distribution table is a table of critical values of the T statistic, which is used to determine whether a sample mean is significantly different from a known population mean. The table is organized by degrees of freedom (df) and alpha levels (α). The degrees of freedom depend on the sample size, and the alpha level determines the level of significance.

Key Components of the Student T Distribution Table

The Student T distribution table consists of the following components:

• Degree of freedom (df): The number of independent observations in the sample, which is typically denoted as n-1, where n is the sample size.
• Alpha level (α): The level of significance, which is typically denoted as 0.01, 0.05, or 0.10.
• Critical value (t): The value of the T statistic that corresponds to the specified alpha level and degrees of freedom.

To use the Student T distribution table, you need to know the degrees of freedom and the alpha level. You can then look up the critical value of the T statistic in the table.

How to Use the Student T Distribution Table

Using the Student T distribution table involves the following steps:

1. Determine the degrees of freedom (df) for your sample. This is typically n-1, where n is the sample size.
2. Specify the alpha level (α) for your test. This is typically 0.01, 0.05, or 0.10.
3. Look up the critical value of the T statistic in the table using the specified degrees of freedom and alpha level.
4. Calculate the T statistic for your sample using the formula: t = (x̄ - μ) / (s / √n), where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
5. Compare the calculated T statistic to the critical value from the table. If the calculated T statistic is greater than the critical value, you reject the null hypothesis. Otherwise, you fail to reject the null hypothesis.

Example Problem

Suppose you want to determine whether the average height of a sample of 20 students is significantly different from the known population mean of 175 cm. You collect a sample of 20 students and calculate a sample mean of 180 cm and a sample standard deviation of 10 cm. Using an alpha level of 0.05, you look up the critical value of the T statistic in the table and find that it is 2.086. You then calculate the T statistic for your sample and find that it is 2.50. Since the calculated T statistic is greater than the critical value, you reject the null hypothesis and conclude that the average height of the sample is significantly different from the known population mean.

In conclusion, the Student T distribution table is a valuable tool for determining the critical values of the T statistic in hypothesis testing. By following the steps outlined in this article, you can use the table to obtain fast answers for various statistical problems.