Find the critical value f 0.025 for F 8, 22

Answer 1

To find the critical value \( f_{0.025} \) for an F-distribution with degrees of freedom \( df_1 = 8 \) and \( df_2 = 22 \), we can look up the value in an F-distribution table or use statistical software. Here we'll use an F-distribution table for common critical values.

The critical value \( f_{0.025} \) corresponds to the value of the F-statistic such that the area to the right is 0.025. This is typically found in the upper-tail of the F-distribution table.

Here's how you can interpret such a table:

1. Locate the row corresponding to the numerator degrees of freedom (\( df_1 = 8 \)).
2. Locate the column corresponding to the denominator degrees of freedom (\( df_2 = 22 \)).
3. Find the intersection of that row and column to get the critical value for the specified significance level.

Using an F-distribution table (or online resource), the critical value \( f_{0.025} \) for \( df_1 = 8 \) and \( df_2 = 22 \) can be found as follows:

- For \( df_1 = 8 \) and \( df_2 = 22 \) at the 0.025 significance level, consult the specific row and column.

However, for more precise calculations or larger/more specific degree of freedom values, statistical software or online calculators (such as those provided by statistical programs like R or Python) are more reliable.

Using an online F-distribution calculator or statistical software, you will find that:

\( f_{0.025, 8, 22} \approx 2.887 \)

So, the critical value \( f_{0.025} \) for \( df_1 = 8 \) and \( df_2 = 22 \) is approximately **2.887**.