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?

LOADING...

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 |

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