Given the confidence interval formular
[tex]\begin{gathered} CI=\bar{x}\pm MOE \\ \bar{x}\Rightarrow\operatorname{mean} \\ \text{MOE}\Rightarrow\text{Margin of error} \\ CI=\text{confidence interval} \end{gathered}[/tex]
Calculate the Margin of error
[tex]\begin{gathered} \text{MOE}=\text{Critical value }\times SE \\ \text{where} \\ SE=\frac{\sigma}{\sqrt[]{n}} \\ \sigma=9.4 \\ n=14 \end{gathered}[/tex][tex]SE=\frac{9.4}{\sqrt[]{14}}=\frac{9.4}{3.7417}=2.5122[/tex][tex]C.V\text{ for 99\% confidence significant level =}2.58[/tex]
Thus, the margin of error is
[tex]\begin{gathered} \text{MOE}=CV\times SE \\ =2.58\times2.5122 \\ =6.48 \end{gathered}[/tex]
The confidence interval from the confidence interval formula will be
[tex]\begin{gathered} CI=\bar{x}\pm MOE \\ =39\pm6.48 \\ =32.52<39<45.48 \end{gathered}[/tex]
Hence, the lower limit of the confidence interval will be 32.52
