Question

Consider the data in the table collected from three independent populations.

Sample 1 Sample 2 Sample 3

   6 1    4

   2 3 5

   7 2 1

   6

​a) Calculate the total sum of squares​ (SST) and partition the SST into its two​ components, the sum of squares between​ (SSB) and the sum of squares within​ (SSW).

b) Use these values to construct a​ one-way ANOVA table.

​c) Using α=0.10​, what conclusions can be made concerning the population​ means?

Click the icon to view a table of critical​ F-scores for α=0.10. ​

a) Determine the values.

SST equals = ​(Type an integer or a​ decimal.)

SSB equals = ​(Type an integer or a​ decimal.)

SSW equals = ​(Type an integer or a​ decimal.)

​b) Complete the​ one-way ANOVA table below.

Source Sum of Squares Degrees of Freedom Mean Sum of Squares F

Between

Within

Total

​(Type integers or decimals. Round to three decimal places as​ needed.)

​c) Let μ1​, μ2​, and μ3 be the population means of samples​ 1, 2, and​ 3, respectively. What are the correct hypotheses for a​ one-way ANOVA​ test?

A. H0​: μ1 = μ2 = μ3

   H1​: μ1≠ μ2 ≠ μ3

B. H0​: μ1 ≠ μ2 ≠ μ3

   H1​: μ1 = μ2 = μ3

C. H0​: μ1 ≠ μ2 ≠ μ3

   H1​: Not all the means are equal.

D. H0​: μ1 = μ2 = μ3

   H1​: Not all the means are equal.

What is the critical​ F-score, Fα​?

Fα = ​(Round to three decimal places as​ needed.)

What is the correct conclusion about the population​ means?

Since the​ F-statistic (does not fall/falls) in the rejection​ region, (reject/ do not reject) H0. The data (do not provide/provide) sufficient evidence to conclude that the population means are not all the same.

Answer 1