SOLUTION: 1. These data are observations collected using a completely randomized design.(You may need to use the appropriate appendix table or technology to answer this question.) Sample

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Question 1207880: 1. These data are observations collected using a completely randomized design.(You may need to use the appropriate appendix table or technology to answer this question.)
Sample 1 Sample 2 Sample 3
3 5 2
2 3 0
4 5 2
3 2 1
2 6
(a) Calculate CM and Total SS. (Round your answer for CM to six decimal places and your Total SS to four decimal places.)
CM =
Total SS =
(b) Calculate SST and MST. (Round your answers to four decimal places.)
SST =
MST =
(c) Calculate SSE and MSE. (Round your answers to four decimal places.)
SSE =
MSE =
(d) Construct an ANOVA table for the data. (Round your answer for F to two decimal places. Round your answers for SS and MS to four decimal places.)
Source df SS MS F
Treatments ______ _______ _____ ______
Error ______ _______ _____ ______
Total ______ _______ _____ ______
(e) State the null and alternative hypotheses for an analysis of variance F-test.
i. H0: 𝜇1 < 𝜇2 < 𝜇3
Ha: 𝜇1 = 𝜇2 = 𝜇3
ii) H0: 𝜇1 = 𝜇2 = 𝜇3
Ha: None of the population means are the same.
iii) H0: One or more pairs of population means differ.
Ha: 𝜇1 = 𝜇2 = 𝜇3
iv) H0: 𝜇1 = 𝜇2 = 𝜇3
Ha: One or more pairs of population means differ.
v) H0: 𝜇1 = 𝜇2 = 𝜇3
Ha: 𝜇1 < 𝜇2 < 𝜇3
(f) Use the p-value approach to determine whether there is a difference in the three population means. (Use 𝛼 = 0.05.)
i) p-value < 0.005
ii) 0.005 < p-value < 0.010
iii) 0.010 < p-value < 0.025
iv) 0.025 < p-value < 0.050
v) 0.050 < p-value < 0.100
vi) p-value > 0.100
g) State your conclusion.
i) H0 is rejected. There is sufficient evidence to indicate a difference among the means.
ii) H0 is not rejected. There is sufficient evidence to indicate a difference among the means.
iii) H0 is not rejected. There is insufficient evidence to indicate a difference among the means.
iv) H0 is rejected. There is insufficient evidence to indicate a difference among the means.
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