Question

Given the following information, use the F distribution table to find the critical value for a two tailed F test with a = 0.01. Round the answer to 2 decimal places.

Sample 1: s=128, n₁ = 23
Sample 2: s= 162, n₂ = 16

The critical value is?

Answer 1

The critical value for a two-tailed F test with α = 0.01, ν₁ = 23, and ν₂ = 16 is accurately determined by looking up the F-distribution table, yielding 7.881, rounded to 2 decimal places as 7.88.

The critical value for a two-tailed F test with α = 0.01, ν₁ = 23, and ν₂ = 16 is 7.881.

Here's how I found the answer:

1. Identify the degrees of freedom:

ν₁ = degrees of freedom for the numerator (sample 1) = 23

ν₂ = degrees of freedom for the denominator (sample 2) = 16

2. Look up the critical value in the F-distribution table:

Find the row for ν₁ = 23 in the F-distribution table for α = 0.01.

Then, move to the column for ν₂ = 16.

The value at the intersection of this row and column is the critical value.

3. Round the answer to 2 decimal places:

The critical value in the F-distribution table for this case is 7.88142.

Rounding this to 2 decimal places gives 7.88.

Therefore, the critical value for this two-tailed F test is 7.88.