Chapter 8, Problem 1P

Find the lower 2.5th percentile of an F distribution with 14 and 7 df. What symbol is used to denote this?

To determine

Find the lower 2.5^th percentile of an F distribution.

Answer to Problem 1P

The lower 2.5^th percentile of an F distribution is 0.296.

Explanation of Solution

The symbol is used to denote lower 2.5^th percentile of an F distribution is,

$F_{n_1-1,n_2-1,\frac{\alpha }{2}}=F_{14,7,0.025}$

Step-by-step procedure to obtain the lower 2.5^th percentile of an F distribution using the MINITAB software:

• Choose Graph > Probability Distribution Plot choose View Probability> OK.
• From Distribution, choose F.
• Enter Numerator df as 14 and Denominator df as 7.
• Click the Shaded Area tab.
• Choose Probability Value and Left Tail for the region of the curve to shade.
• Enter the Probability Value as 0.025.
• Click OK.

Output using the MINITAB software is given below:

From the output, the lower 2.5^th percentile of an F distribution is 0.296.