Question

Consider the data in the table collected from four independent populations.		Sample 1	Sample 2	Sample 3	Sample 4
​a) Calculate the total sum of squares​ (SST). ​b) Partition the SST into its two​ components, the sum of squares between​ (SSB) and the sum of squares within​ (SSW).		44	1414	2121	44
		77	1111	2222	33
		88	1717	2020	1111
		66		1313

​c) Using

alphaαequals=0.050.05​,

what conclusions can be made concerning the population​ means?

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

alphaαequals=0.050.05.

​a) Determine the value of SST.

SSTequals=nothing

​(Type an integer or a​ decimal.)

​b) Determine the values of SSB and SSW.

SSBequals=nothing

​(Type an integer or a​ decimal.)

SSWequals=nothing

​(Type an integer or a​ decimal.)​c) Let

mu 1μ1​,

mu 2μ2​,

mu 3μ3​,

and

mu 4μ4

be the population means of samples​ 1, 2,​ 3, and​ 4, respectively. What are the correct hypotheses for a​ one-way ANOVA​ test?

A.

Upper H 0H0​:

Not all the means are equal.

Upper H 1H1​:

mu 1μ1equals=mu 2μ2equals=mu 3μ3equals=mu 4μ4

B.

Upper H 0H0​:

mu 1μ1not equals≠mu 2μ2not equals≠mu 3μ3not equals≠mu 4μ4

Upper H 1H1​:

mu 1μ1equals=mu 2μ2equals=mu 3μ3equals=mu 4μ4

C.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2equals=mu 3μ3equals=mu 4μ4

Upper H 1H1​:

mu 1μ1not equals≠mu 2μ2not equals≠mu 3μ3not equals≠mu 4μ4

D.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2equals=mu 3μ3equals=mu 4μ4

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​ F-test statistic for this​ test?

Answer 1

(a) SST = 8,685.21

(b) SSB = 6,993.80

SSW = 1,691.42

(c) The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: Not all the means are equal

The critical​ F-score = 3.708

F-test statistic = 13.78

Sample 1	Sample 2	Sample 3	Sample 4
44	14	21	44
77	11	22	33
88	17	20	11
66		13
	Mean	n	Std. Dev
	68.8	4	18.79	Sample 1
	14.0	3	3.00	Sample 2
	19.0	4	4.08	Sample 3
	29.3	3	16.80	Sample 4
	34.4	14	25.85	Total
ANOVA table
Source	SS	df	MS	F	p-value	Critical F
Treatment	6,993.80	3	2,331.27	13.78	.0007	3.708
Error	1,691.42	10	169.142
Total	8,685.21	13