Question

Consider the data in the table collected from three independent populations.		Sample 1	Sample 2	Sample 3
		33	11	88
​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).		66	33	22
		99	88	33
				1111

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

​c) Using

alphaαequals=0.100.10​,

what conclusions can be made concerning the population​ means?

LOADING...

Click the icon to view a table of critical​ F-scores for

alphaαequals=0.100.10.

​a) Determine the values.

SSTequals=nothing

​(Type an integer or a​ decimal.)

SSBequals=nothing

​(Type an integer or a​ decimal.)

SSWequals=nothing

​(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	nothing	nothing	nothing	nothing
Within	nothing	nothing	nothing
Total	nothing	nothing

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

​c) Let

mu 1μ1​,

mu 2μ2​,

and

mu 3μ3

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

A.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2equals=mu 3μ3

Upper H 1H1​:

mu 1μ1not equals≠mu 2μ2not equals≠mu 3μ3

B.

Upper H 0H0​:

mu 1μ1not equals≠mu 2μ2not equals≠mu 3μ3

Upper H 1H1​:

Not all the means are equal.

C.

Upper H 0H0​:

mu 1μ1not equals≠mu 2μ2not equals≠mu 3μ3

Upper H 1H1​:

mu 1μ1equals=mu 2μ2equals=mu 3μ3

D.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2equals=mu 3μ3

Upper H 1H1​:

Not all the means are equal.What is the critical​ F-score,

Upper F Subscript alphaFα​?

Upper F Subscript alphaFαequals=nothing

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

What is the correct conclusion about the population​ means?

Since the​ F-statistic

▼

falls

does not fall

in the rejection​ region,

▼

do not reject

reject

Upper H 0H0.

The data

▼

do not provide

provide

sufficient evidence to conclude that the population means are not all the same.

Click to select your answer(s).

Answer 1

Applying ANOVA:

a)

SST =106.4

SSB=8.40

SSW=98

b)

Source	SS	df	MS	F
Between	8.40	2	4.200	0.300
Within	98.00	7	14.000
Total	106.40	9

c)

H0: μ1 = μ2 = μ3

H1: not all the means are equal

critical​ F-score =Falpha =3.257

Since the​ F-statistic does not fall in the rejection​ region, , do not reject Ho

The data do not provide sufficient evidence to conclude that the population means are not all the same.