Problem

Find the margin of error for the given values of $\mathrm{c}, \sigma$, and $\mathrm{n}$. \[ c=0.95, \sigma=3.2, n=64 \] Click the icon to view a table of common critical values. $E=\square$ (Round to three decimal places as needed.) Table of Common Critical Values \begin{tabular}{c|c} \begin{tabular}{c} Level of \\ Confidence \end{tabular} & $\mathbf{z}_{\boldsymbol{c}}$ \\ \hline $90 \%$ & 1.645 \\ $95 \%$ & 1.96 \\ $99 \%$ & 2.575 \end{tabular}

Solution

Step 1 :Given values are: confidence level (c) = 0.95, standard deviation (σ) = 3.2, and sample size (n) = 64.

Step 2 :From the table of common critical values, the critical value (zc) for a 95% confidence level is 1.96.

Step 3 :The formula to calculate the margin of error (E) is: \(E = zc \times \frac{σ}{\sqrt{n}}\)

Step 4 :Substitute the given values into the formula: \(E = 1.96 \times \frac{3.2}{\sqrt{64}}\)

Step 5 :Simplify the expression to find the margin of error (E): \(E = 0.784\)

Step 6 :\(\boxed{0.784}\) is the margin of error for the given values of c, σ, and n.

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