91Ó°ÊÓ

The level of support for corporate sustainability was obtained for each in a sample of 992 senior managers at CPA firms. So, the sample size is 992.

From the given MINITAB output, the 90% confidence interval is (672,779). Thus, the variance of level of support for all senior managers at CPA firms lies between 672 points squared and 779 points squared at 90% confidence.

b.

Since, the$\mathbf{100}\mathbf{(}\mathbf{1}\mathbf{−}\mathbf{Î\pm }\mathbf{)}\mathit{\%}$ confidence interval is given as,

$\mathbf{(}\frac{\mathbf{(}\mathbf{n}\mathbf{−}\mathbf{1}\mathbf{)}{\mathbf{s}}^{\mathbf{2}}}{{\mathbf{χ}}_{\mathbf{0}\mathbf{.05}\frac{\mathbf{Î\pm }}{\mathbf{2}}}^{\mathbf{2}}}\mathbf{≤}{\mathbf{σ}}^{\mathbf{2}}\mathbf{≤}\frac{\mathbf{(}\mathbf{n}\mathbf{−}\mathbf{1}\mathbf{)}{\mathbf{s}}^{\mathbf{2}}}{{\mathbf{χ}}_{\mathbf{0}\mathbf{.95}}^{\mathbf{2}}}\mathbf{)}$

Let the confidence level be,

$\begin{array}{c}1−\mathrm{Î\pm }=0.90\\ \mathrm{Î\pm }=1−0.90\\ =0.10\end{array}$

Therefore,

$\frac{\mathrm{Î\pm }}{2}=0.05$

Also, the degrees of freedom is $(n−1)=991$

Now, from table critical-values are,

$\begin{array}{l}{\mathrm{χ}}_{0.05}^2\left(991\right)=1065.3\\ {\mathrm{χ}}_{0.95}^2\left(991\right)=918.90\end{array}$

Therefore,

role="math" localid="1658299573144" $\begin{array}{c}(\frac{(n−1)s^2}{{\mathrm{χ}}_{0.05\frac{\mathrm{Î\pm }}{2}}^2}≤{\mathrm{σ}}^2≤\frac{(n−1)s^2}{{\mathrm{χ}}_{0.95}^2})=(\frac{(992−1)772}{1065.3}≤{\mathrm{σ}}^2≤\frac{(992−1)722}{918.90})\\ =(\frac{\left(991\right)772}{1065.3}≤{\mathrm{σ}}^2≤\frac{\left(991\right)722}{918.90})\\ =(671.6≤{\mathrm{σ}}^2≤778.6)\end{array}$

Hence, the 90% confidence interval for${\mathrm{σ}}^2$ is (671.6, 778.6).

Yes, this result is near to the interval shown in the printout.

From the given MINITAB output, the 90% confidence interval forthe standard deviation of level of support for $\mathrm{σ}$all senior managers at CPA firms lies between 25.9 points and 27.9 points.

From part a, the 90% confidence interval is (672,779). Take the square root on the lower and upper limit. That is,

$(\sqrt{672},\sqrt{779})=(25.9,27.9)$

This result is same as the interval shown in the printout.

The 90% confidence interval for the standard deviation of level of support for all senior managers at CPA firms lies between 25.9 points and 27.9 points.

f.

To ensure the appropriateness of the level of support for all senior managers at CPA firms of the population must possess the normal distribution. Thus, it can be concluded that the distribution of the data is approximately normal since the normal probability plot do not shows deviation from the line.