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Chapter 10: Q40SE (page 435)
Refer to Exercise 38. What is b for the test when true average DNA content is identical for three of the diets and falls below this common value by 1 standard deviation (s) for the other two diets?
\(\beta \approx 0.52\)
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In an experiment to compare the tensile strengths of different type of\({\bf{I = 5}}\) copper wire, \({\bf{J = 4}}\) samples of each type were used. The between-samples and within- sample estimates of \({{\bf{\sigma }}^{\bf{2}}}\) were computed as \({\bf{MS}}{{\bf{T}}_{\bf{r}}}{\bf{ = 2673}}{\bf{.3}}\) and respectively. Use the F test at level. to test \({{\bf{H}}_{\bf{0}}}\,{\bf{:}}\,\,{{\bf{\mu }}_{\bf{1}}}{\bf{ = }}{{\bf{\mu }}_{\bf{2}}}{\bf{ = }}{{\bf{\mu }}_{\bf{3}}}{\bf{ = }}{{\bf{\mu }}_{\bf{4}}}{\bf{ = }}{{\bf{\mu }}_{\bf{5}}}\)versus \({{\bf{H}}_{\bf{a}}}{\bf{:}}\)at least two \({{\bf{\mu }}_{\bf{i}}}{\bf{'s}}\) are unequal.
consider the accompanying data on plant growth after the application of five different types of growth hormone.
\(\begin{aligned}{l}1:\\2:\\3:\\4:\\5:\end{aligned}\) \(\begin{aligned}{l}13\\21\\18\\7\\6\,\end{aligned}\) \(\begin{aligned}{l}17\\13\\15\\11\\11\,\,\end{aligned}\) \(\begin{aligned}{l}7\\20\\20\\18\\15\,\,\end{aligned}\) \(\begin{aligned}{l}14\\17\\17\\10\\8\end{aligned}\)
it is common practice in many countries to destroy (shred)refrigerators at the end of their usefull lives.In this process material from insulating foam may be released into the atmosphere.The article 鈥淩elease of fluorocarbons from Insulation foam in Home Appliances During shredding鈥�(J.of the Air and waste Mgmt.Assoc.,2007:1452-1460)gave the following data on foam density(g/L)For each of two refrigerators produced by four different manufactures:
\(\begin{aligned}{l}1.30.4,\,29.2\,\,\,\,\,2.27.7,27.1\\3.27.1,24.8\,\,\,\,\,\,4.25.5,28.8\end{aligned}\)
Does it appear that true average foam density is not the same for all these manufacture?carry out an appropriate test of hypotheses by obtaining as much p-value information as possible,and summarize your analysis in an ANOVA table.
When sample sizes are equal\(\left( {{J_i} = J} \right)\), the parameters\({\alpha _1},{\alpha _2},...{\alpha _I}\,\)of the alternative parameterization are restricted by\(\Sigma {\alpha _i} = 0\). For unequal sample sizes, the most natural restriction is\(\Sigma {J_i}{\alpha _i} = 0\). Use this to show that
\(E\left( {MSTr} \right) = {\alpha ^2} + \frac{1}{{I - 1}}\Sigma {J_i}\alpha _i^2\)
What is\(E\left( {MSTr} \right)\)when\({H_0}\)is true? (This expectation is correct if\(\Sigma {J_i}{\alpha _i} = 0\,\)is replaced by the restriction\(\Sigma {\alpha _i} = 0\)(or any other single linear restriction on the ai 鈥檚 used to reduce the model to I independent parameters), but\(\Sigma {J_i}{\alpha _i} = 0\)simplifies the algebra and yields natural estimates for the model parameters (in particular,\({\mathop {\,\,\,\,\alpha }\limits^{\,\,\,\,\,\^} _i} = {\mathop X\limits^\_ _i}\, - \,\mathop X\limits^\_ ..\,\,\,\,{H_0}\)).)
Apply the modified Tukey鈥檚 method to the data in Exercise 22 to identify significant differences among the\({\mu _i}\)鈥檚.
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