To determine which of the given combinations of [tex]\( z \)[/tex]-values, standard deviations [tex]\( s \)[/tex], and sample sizes [tex]\( n \)[/tex] result in a margin of error (ME) of 0.95, we will use the given margin of error formula:
[tex]\[
ME = \frac{z \cdot s}{\sqrt{n}}
\][/tex]
Let's examine each combination step-by-step:
1. Combination 1: [tex]\( z = 2.14 \)[/tex], [tex]\( s = 4 \)[/tex], [tex]\( n = 9 \)[/tex]
[tex]\[
ME = \frac{2.14 \cdot 4}{\sqrt{9}} = \frac{8.56}{3} = 2.8533\ldots
\][/tex]
Margin of Error (ME) = 2.8533 (approx). This does not equal 0.95.
2. Combination 2: [tex]\( z = 2.14 \)[/tex], [tex]\( s = 4 \)[/tex], [tex]\( n = 81 \)[/tex]
[tex]\[
ME = \frac{2.14 \cdot 4}{\sqrt{81}} = \frac{8.56}{9} = 0.9511\ldots
\][/tex]
Margin of Error (ME) = 0.9511 (approx). This does not exactly equal 0.95.
3. Combination 3: [tex]\( z = 2.14 \)[/tex], [tex]\( s = 16 \)[/tex], [tex]\( n = 9 \)[/tex]
[tex]\[
ME = \frac{2.14 \cdot 16}{\sqrt{9}} = \frac{34.24}{3} = 11.4133\ldots
\][/tex]
Margin of Error (ME) = 11.4133 (approx). This does not equal 0.95.
4. Combination 4: [tex]\( z = 2.14 \)[/tex], [tex]\( s = 16 \)[/tex], [tex]\( n = 81 \)[/tex]
[tex]\[
ME = \frac{2.14 \cdot 16}{\sqrt{81}} = \frac{34.24}{9} = 3.8044\ldots
\][/tex]
Margin of Error (ME) = 3.8044 (approx). This does not equal 0.95.
We have evaluated all the combinations, and none of them result in a margin of error of exactly 0.95. Therefore, none of the given combinations produce the desired margin of error.
Thus, the answer is:
[tex]\[
\boxed{[]}
\][/tex]
