91Ó°ÊÓ

The formula to calculate the level of confidence, the confidence interval for the mean is:

$\stackrel{¯}{X}{\text{±³ú}}_{\text{1}}\text{=}\mathrm{Î\pm }\text{/}2\left(\frac{\mathrm{σ}}{\sqrt{\text{n}}}\right)$

We will calculate the level of confidence for each provided confidence interval using the score of the multiplied or the important test statistic.

The calculation is given below:

$$\begin{gathered} {\text{z}}_{\text{1}}=\mathrm{Î\pm }/2=1.96 \\ \text{1}-\mathrm{Î\pm }/2=0.975 \\ \mathrm{Î\pm }=0.05 \end{gathered}$$

Therefore,

$$\begin{gathered} \left(1-\mathrm{Î\pm }\right)×100\% \\ =95\% \end{gathered}$$

Hence, the level of confidence is 95%

$$\begin{gathered} {\text{z}}_{\text{1}}=\mathrm{Î\pm }/2=1.645 \\ 1-\mathrm{Î\pm }/2=0.95 \\ \mathrm{Î\pm }=10 \end{gathered}$$

Therefore,

$$\begin{gathered} \left(1-\mathrm{Î\pm }\right)×100\% \\ =90\% \end{gathered}$$

Hence, the level of confidence is 90%

$$\begin{gathered} {\text{z}}_{\text{1}}=\mathrm{Î\pm }/2=2.575 \\ \text{1}-\mathrm{Î\pm }/2=0.995 \\ \mathrm{Î\pm }=0.01 \end{gathered}$$

Therefore,

$$\begin{gathered} \left(1-\mathrm{Î\pm }\right)×100\% \\ =99\% \end{gathered}$$

Hence, the level of confidence is 99%

Step 3: (d) The data is given below

$$\begin{gathered} {\text{Here, test stastticsZ}}_{\text{cr}}\text{=1.282} \\ \text{Confidence level=80\%} \end{gathered}$$

Hence, the level of confidence is 80%

Step 3: (e) The data is given below

$$\begin{gathered} {\text{z}}_{\text{1}}\text{=}\mathrm{Î\pm }\text{/}2=0.99 \\ 1-\mathrm{Î\pm }\text{/}2=0.839 \\ \mathrm{Î\pm }=0.322 \end{gathered}$$

Therefore,

$$\begin{gathered} \left(1-\mathrm{Î\pm }\right)×100\% \\ =67.8\% \end{gathered}$$

Hence, the level of confidence is 67.8%