The following ANOVA table, based on information obtained for three samples selec
ID: 3243396 • Letter: T
Question
The following ANOVA table, based on information obtained for three samples selected from three independent populations that are normally distributed with equal variances, has a few missing values.
Source of
Variation
Degrees of
Freedom
Sum of
Squares
Mean
Square
Value of the
Test Statistic
Between
2
II
19.2813
Within
89.3677
III
F = ___V__ = VII
VI
Total
12
IV
a) Find the missing values and complete the ANOVA table. Round to four decimal places.
b) Using = .01, what is your conclusion for the test with the null hypothesis that the means of the three populations are all equal against the alternative hypothesis that the means of the three populations are not all equal?
i. Reject H0. Conclude that the means of the three populations are equal.
ii. Reject H0. Conclude that the means of the three populations are not equal.
iii. Do not reject H0. Conclude that the means of the three populations are equal.
iv. Do not reject H0. Conclude that the means are of the three populations are not equal.
Source of
Variation
Degrees of
Freedom
Sum of
Squares
Mean
Square
Value of the
Test Statistic
Between
2
II
19.2813
Within
89.3677
III
F = ___V__ = VII
VI
Total
12
IV
Explanation / Answer
(a)
(I) within df=total df-between df=12-2=10 ( df=degree of freedom)
(II)sum of square(SS)=Mean Square(MS)*df
so Between SS=19.2813*2=38.5626
(III)Mean Square(MS)=Sum of Square/df
Within MS=89.3677/10=8.9368
(IV) Total SS=between SS+Within SS=38.5626+89.3677=127.9303
(V)F=BEtween MS/Within MS=19.2813/8.9367=2.16
(VI) critical F(0.01,2,10)=7.56
(b) since critical F=7.56 is more than calcuated F=2.16 , so we fail to reject H0 and conclude that
Conclude that the means of the three populations are equal.
right choice is iii. Do not reject H0. Conclude that the means of the three populations are equal.
Source of Degrees of Sum of Mean Value of the Variation Freedom Squares Square Test Statistic Between 2 38.5626 19.2813 Within 10 89.3677 8.93677 2.157524475 Total 12 127.9303 7.5594