91影视

Hypotheses are typically written in the form of if/then statements, such as if someone consumes a lot of sugar, they will develop cavities in their teeth.

a) plausible that the variances of the five axial stiffness index.

The fact that the following is true

\({S_4} = 44.51 > 2.20.83 = 2.{S_3}\)

b) To test the relevant hypotheses.

you can conclude that the population variances are equal (this stands).

The hypotheses of interest are

\({H_0}:{\mu _i} = {\mu _j}\,,i \ne j\)

versus alternative hypothesis

\({H_a}:\)at least two of the are different

The value of F statistic is given, and it is \(f = 10.48;\)

Thus the P value is the area under the F curve to the right of f which can be found at the appendix.

\(P(F > f) = 0\)

e has degrees of freedom \(4\,\,and\,30\) (given in the exercise). Hence,

reject null hypothesis

there is difference in axial stiffness for the different plate lengths.

c) construct the corresponding underscoring pattern.

The T Method for Identifying Significantly Different 渭i 鈥檚

Find value \({Q_{\alpha ,}}I,{I_{\left( {j - 1} \right)}}\)at the Table A.10. in the appendix of the book for given \(\alpha \).

Compute and list the sample means in increasing order. Calculate

\(w = {Q_{\alpha ,}}I,{I_{\left( {j - 1} \right)}}.\sqrt {\frac{{MSE}}{J}} \)

underline pairs of the sample means that differ by less than W . The pair of sample which are not underscored by the same line corresponding of population or treatment means that they are significantly different.

From the mentioned table, and\(\alpha = 0.05\)\(I = 5,J = 7\)

\({Q_{\alpha ,}}I,{I_{\left( {J - 1} \right)}} = {Q_{0.05,5,30}} = 4.1\)

The value of of estimate using the table.

\(MSE = 10.43\)

Compute the w value as

\(w = {Q_{\alpha ,}}I,{I_{\left( {j - 1} \right)}}.\sqrt {\frac{{MSE}}{J}} = 4.1.\sqrt {\frac{{1049}}{7}} = 50.79\)

The differences can be computed manually very easy; they are also given in the table in the exercise.

Difference between means that are smaller than\(w = 50.79\)it is clear which are smaller the part. conclusion is that three group have been created, first group containing axial stiffness\(3,6\,\,and\,\,8\) a second group containing axial stiffness\(6,8\,\,and\,10\)third group containing axial stiffness \(10,12\) between the group there is significant difference but within the groups there are no significant differences. This can be represented using line .

\(\begin{aligned}{l}\,\,\,\,\,{\overline x _{1.}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{2.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{3.}}\\\underline {333.21\,\,\,\,\,368.06\,\,\,\,\,\,375.13\,\,\,\,} \end{aligned}\) \(\underline \begin{aligned}{l}\,\,\,\,{\overline x _{4.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{5.}}\,\\407.36\,\,\,\,437.17\,\,\,\end{aligned} \,\,\,\)

Hence,

\(\begin{aligned}{l}\,\,\,\,\,{\overline x _{1.}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{2.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{3.}}\\\underline {333.21\,\,\,\,\,368.06\,\,\,\,\,\,375.13\,\,\,\,} \end{aligned}\) \(\underline \begin{aligned}{l}\,\,\,\,{\overline x _{4.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{5.}}\,\\407.36\,\,\,\,437.17\,\,\,\end{aligned} \,\,\,\)