Question

Consider the data in the table collected from four
independent populations. The conclusion of a one-way ANOVA test
using
alphaαequals=0.05 is that the population means are not all the same. Determine which means are different usingalphaαequals=0.05 |
Sample 1 |
Sample 2 |
Sample 3 |
Sample 4 |
||
---|---|---|---|---|---|---|

6 |
13 |
23 |
9 |
|||

7 |
16 |
13 |
8 |
|||

8 |
19 |
19 |
10 |
|||

9 |
22 |

Click here to view the ANOVA summary table.

Find the Tukey-Kramer critical range CR for each of these differences.

CR1,2 |
equals= |
? |
CR2,3 |
equals= |
? |

CR1,3 |
equals= |
? |
CR2,4 |
equals= |
? |

CR1,4 |
equals= |
? |
CR3,4 |
equals= |
? |

(Round to two decimal places as needed.)

Answer #1

Applying One way ANOVA from excel: data-data analysis: ANOVA(one factor):

Source of Variation |
SS |
df |
MS |
F |

Between Groups | 352.25 | 3 | 117.4167 | 13.69291 |

Within Groups | 85.75 | 10 | 8.575 | |

Total | 438 | 13 |

from above:

MSE= | 8.575 | ||

df(error)= | 10 | ||

number of treatments = | 4 | ||

pooled standard deviation=Sp =√MSE= | 2.928 |

critical q with 0.05 level and k=4, N-k=10 df= | 4.33 | ||

Tukey's (HSD) =(q/√2)*(sp*√(1/ni+1/nj) = |

**CR _{1-2}
=(4.33/sqrt(2))*(2.928)*sqrt(1/4+1/3)=6.85**

**CR _{1-3} =6.34**

**CR _{1-4} =6.85**

**CR _{2-3} =6.85**

**CR _{2-4} =7.32**

**CR _{3-4} =6.85**

The conclusion of a one-way ANOVA procedure for
the data shown in the table is to reject the null hypothesis that
the means are all equal. Determine which means are different using
alpha α equals=.05
Sample 1
Sample 2
Sample 3
88
1515
2020
1515
1414
2424
77
1717
2222
99
1313
1919
LOADING...
Click the icon to view the ANOVA summary table.
LOADING...
Click the icon to view a studentized range table for
alphaαequals=0.050.05.
Let
x overbarx1,
x overbarx2,...

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...

Consider the data in the table collected from three independent
populations.
Sample 1 Sample 2 Sample 3
6 1 4
2 3 5
7 2 1
6
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).
b) Use these values to construct a one-way ANOVA table.
c) Using α=0.10, what conclusions can be made concerning...

Consider the data in the table collected from four independent
populations. a=0.10
Sample 1- 19, 12, 14, 17
Sample 2- 13, 19, 10
Sample 3- 17, 14, 16, 8
Sample 4- 8, 13, 9
a) Determine the value of SST. (Round to one decimal place as
needed.)
b) Determine the values of SSB and SSW. (Round to one decimal
place as needed.)
c) What is the critical F-score, Fα? (Round to three decimal
places as needed.)
d) What is the...

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numbers 1, 2, 3, and 4 according to this table:
side of die 1 2 3 4 5 6 7 8 9 10 number displayed 1 1 1 1 2 2 2 3 3
4
Rolling two such dice is an experiment with the sample space S =
(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1)
(3,2) (3,3) (3,4) (4,1) (4,2) (4,3)...

Consider the data in the table collected from three independent
populations.
Sample_1 - 10,3,8 Sample_2 - 5,1,6 Sample_3- 4,6,3,7
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).
b) Use these values to construct a one-way ANOVA table.
c) Using alphaequals0.05, what conclusions can be made
concerning the population means?
alphaequals0.05.
a) Determine the values. SSTequals ___ (Type an...

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...

Consider the following data for two independent random samples
taken from two normal populations.
Sample 1
10
7
13
7
9
8
Sample 2
8
7
8
4
6
9
(a)Compute the two sample means.
Sample 1:
Sample 2:
(b)Compute the two sample standard deviations. (Round your
answers to two decimal places.)
Sample 1:
Sample 2:
(c) What is the point estimate of the difference between the two
population means? (Use Sample 1 − Sample 2.)
(d) What is the...

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left blank) for the amount of food (kidney, shrimp, chicken liver,
salmon and beef) consumed by 50 randomly assigned cats (10 per
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H0: All the 5 population means are equal
H1: At least one population mean is
different.
Population: 1 = Kidney, 2 = Shrimp, 3 = Chicken Liver, 4 =
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ANOVA
Source of Variation
SS
df
MS
F
P-value
F...

Consider the partial ANOVA table shown below. Let a = .01
Source of Variation
DF
SS
MS
F
Between Treatments
3
180
Within Treatments (Error)
Total
19
380
If all the samples have five observations each:
there are 10 possible pairs of sample means.
the only appropriate comparison test is the Tukey-Kramer.
all of the absolute differences will likely exceed their
corresponding critical values.
there is no need for a comparison test – the null hypothesis is
not rejected.
2...

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