In a completely randomized design, eight experimental units were used for each of the five levels of the factor. Consider the following ANOVA table. Source of Variation Treatments Error Total Sum of Squares 300 110 410 Degrees of Freedom 4 Ho: M₁ M₂ M3 M4 M5 # на: М1 = М2 = из =H4=H5 35 (a) What hypotheses are implied in this problem? O Ho: Not all the population means are equal. Ha: M₁ = M₂ = M3 = μ4 = μ5 о но: 11 = H2= M3 =H4 = M5 Ha: M₁ M₂ M3 M4 M5 39 Ho: M₁ = M₂ = μ3 = H4 = 5 H₂: Not all the population means are equal. Mean Square 75 O Ho: At least two of the population means are equal. Ha: At least two of the population means are different. 3.14 F p-value 23.86 0.0000 (b) At the α = 0.05 level of significance, can we reject the null hypothesis in part (a)? Explain. O Because the p-value > a = 0.05, we cannot reject Ho. O Because the p-value ≤ α = 0.05, we cannot reject Ho. O Because the p-value> x = 0.05, we can reject Ho. O Because the p-value ≤ α = 0.05, we can reject Ho

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
In a completely randomized design, eight experimental units were used for each of the five levels of the factor. Consider the following ANOVA table.
Source
of Variation
Treatments
Error
Total
Sum
of Squares
300
110
410
Degrees
of Freedom
#
#
Ho: M₁ M₂ M3 M4 M5
M5
На: M1 = M2 = M3=M4
4
(a) What hypotheses are implied in this problem?
Ho: Not all the population means are equal.
Ha: M₁ = M₂ = M3 = M4 = M5
=
35
Ho: M₁ = M₂ = M3 = M4 = M5
H₂: Not all the population means are equal.
Ho: M₁ = M₂ = M3 = μ₁4 = M5
Ha: M₁ M₂ M3 M4 M5
# # #
39
Mean
Square
Ho:
: At least two of the population means are equal.
H₂: At least two of the population means are different.
75
3.14
F
23.86
p-value
0.0000
(b) At the α = 0.05 level of significance, can we reject the null hypothesis in part (a)? Explain.
Because the p-value > α = 0.05, we cannot reject Ho.
Because the p-value < α = 0.05, we cannot reject Ho.
Because the p-value > α = 0.05, we can reject Ho.
Because the p-value ≤ a = 0.05, we can reject Ho.
Transcribed Image Text:In a completely randomized design, eight experimental units were used for each of the five levels of the factor. Consider the following ANOVA table. Source of Variation Treatments Error Total Sum of Squares 300 110 410 Degrees of Freedom # # Ho: M₁ M₂ M3 M4 M5 M5 На: M1 = M2 = M3=M4 4 (a) What hypotheses are implied in this problem? Ho: Not all the population means are equal. Ha: M₁ = M₂ = M3 = M4 = M5 = 35 Ho: M₁ = M₂ = M3 = M4 = M5 H₂: Not all the population means are equal. Ho: M₁ = M₂ = M3 = μ₁4 = M5 Ha: M₁ M₂ M3 M4 M5 # # # 39 Mean Square Ho: : At least two of the population means are equal. H₂: At least two of the population means are different. 75 3.14 F 23.86 p-value 0.0000 (b) At the α = 0.05 level of significance, can we reject the null hypothesis in part (a)? Explain. Because the p-value > α = 0.05, we cannot reject Ho. Because the p-value < α = 0.05, we cannot reject Ho. Because the p-value > α = 0.05, we can reject Ho. Because the p-value ≤ a = 0.05, we can reject Ho.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman