For an independent-measures ANOVA comparing three treatments with a sample of

n = 5 in each treatment, what is the critical value for the F-ratio using α = .05?

a. 3.88
b. 3.49
c. 3.74
d. 3.34

F(0.05, 2, 12) = 3.88.

To determine the critical value for the F-ratio, we need to find the appropriate F-value from an F-table. The critical value depends on the degrees of freedom of the numerator and denominator.

In this case, for an independent-measures ANOVA comparing three treatments with a sample size of n = 5 in each treatment, the degrees of freedom are as follows:

- Numerator degrees of freedom (df between groups): k - 1 = 3 - 1 = 2
- Denominator degrees of freedom (df within groups): N - k = 15 - 3 = 12

Using α = 0.05, the critical value for the F-ratio can be found in the F-table with 2 degrees of freedom for the numerator and 12 degrees of freedom for the denominator.

After referring to the F-table, we find that the critical value for α = 0.05 is approximately 3.49.

Therefore, the correct answer is b. 3.49.

To find the critical value for the F-ratio, we need to know the degrees of freedom for the numerator and denominator.

In an independent-measures ANOVA with three treatments and n = 5 in each treatment, there will be two groups of degrees of freedom - the degrees of freedom for the numerator (df₁) and the degrees of freedom for the denominator (df₂).

The degrees of freedom for the numerator (df₁) is equal to the number of treatments minus one, which in this case is 3 - 1 = 2.

The degrees of freedom for the denominator (df₂) is equal to the total number of data points minus the number of treatments, which is (n × number of treatments) - number of treatments = 5 × 3 - 3 = 12.

Now, we can use these degrees of freedom to find the critical value for the F-ratio. Since α = .05, we want to find the F-value that corresponds to a cumulative probability of .95 (1 - α) in the F-distribution.

Using a statistical table or a calculator, we can find that the critical value for the F-ratio with df₁ = 2 and df₂ = 12 at α = .05 is approximately 3.88.

Therefore, the correct answer is a. 3.88.