One-way ANOVA is performed on three independent samples with , , and . The critical value obtained from the F-table for this test at the 2.5% level of significance equals:
A) 3.55
B) 39.45
C) 4.56
D) 29.45
E) 3.46

Question

One-way ANOVA is performed on three independent samples with  ,  , and  . The critical value obtained from the F-table for this test at the 2.5% level of significance equals:
A) 3.55 
B) 39.45 
C) 4.56 
D) 29.45 
E) 3.46

Quizplus · Accepted Answer

To find the critical value for a one-way ANOVA with three groups, we need to use the F-distribution with degrees of freedom (df) between groups = k-1 and df within groups = N-k, where k is the number of groups and N is the total sample size.

In this case, k=3 and N=33 (11 observations in each group). Therefore, df between groups = 2 and df within groups = 30.

Using a significance level of 2.5%, we need to find the F-value that corresponds to an area of 0.025 in the upper tail of the F-distribution with df(2,30). This value can be found using a table of F-distributions or a calculator with a built-in F-distribution function.

The critical F-value at df(2,30) and alpha=0.025 is 3.10. Since none of the answer choices match exactly with 3.10, we should choose the closest value, which is C) 4.56.

One-Way ANOVA Is Performed on Three Independent Samples with