Question

Consider the partially completed​ one-way ANOVA summary table below.

​a) Complete the remaining entries in the table. ​

b) How many population means are being​ tested?

​c) Using α=0.05​, what conclusions can be made concerning the population​ means?

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

Between    ​? 4    ​? ​?

Within    60 ​ ? ​?

Total    160 14 LOADING...

Click the icon to view a table of critical​ F-scores for alpha α=0.05. ​

a) Complete the ANOVA table below.

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

Between    ? 4 ?    ?

Within    60    ?    ?

Total 160    14

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

b) There are (What) population means being tested.

​c) What are the hypotheses for this​ test?

A. H0​: Not all the means are equal. H1​: All the means are equal.

B. H0​: None of the means are equal. H1​: All the means are equal.

C. H0​: All the means are equal. H1​: None of the means are equal.

D. H0​: All the means are equal. H1​: Not all the means are equal.

Determine the critical​ F-score, Fα​, for this test.

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

State the conclusion for alpha α= 0.05. S

ince the​ F-test statistic is (greater/ less) than the critical​ F-score, (reject/do not reject)he null hypothesis and conclude that (ll of the population means are the same/at least one of of the population means is different)

Answer 1

SOLUTION a: Complete ANOVA TABLE :

SOURCE	S.S	DF	MS	F
BETWEEN	100-60=100	4	100/4=25	25/6=4.17
WITHIN	60	14-4=10	60/10=6
ERROR	160	14

b) Total number of treatments = degrees of freedom(Between)+1= 4+1=5

c) D. H0​: All the means are equal. H1​: Not all the means are equal.

Degrees of freedom 1= 4 and Degrees of freedom 2=10

F critical=3.478

Since the​ F-test statistic is greater than the critical​ F-score, reject the null hypothesis and conclude that at least one of of the population means is different.