To solve this problem, we just need to use the margin of error formula. This formula is given by
[tex]ME=z\times\frac{\sigma}{\sqrt[]{n}}[/tex]
Where ME is our margin of error, sigma is the standard deviation, n is the sample size, and z is the critical value(associated with the confidence level).
From the text, we have:
[tex]\begin{gathered} n=23 \\ \sigma=13.7 \\ z(0.80)=1.32 \end{gathered}[/tex]
Plugging those values in our equation, we have
[tex]ME=1.32\times\frac{13.7}{\sqrt[]{23}}=\frac{18.084}{\sqrt[]{23}}=3.77077466381\ldots\approx3.8[/tex]
And this is our margin of error.
