which of the following z - values, standard deviations, and sample sizes produce a margin of error of…

Explanation:

Step1: Recall the margin - of - error formula

$ME=\frac{z\cdot s}{\sqrt{n}}$

Step2: Test the first option

For $z = 2.14$, $s = 4$, $n = 9$, we have $\sqrt{n}=\sqrt{9}=3$, and $ME=\frac{2.14\times4}{3}=\frac{8.56}{3}\approx2.85$

Step3: Test the second option

For $z = 2.14$, $s = 4$, $n = 81$, $\sqrt{n}=\sqrt{81}=9$, and $ME=\frac{2.14\times4}{9}=\frac{8.56}{9}\approx0.95$

Step4: Test the third option

For $z = 2.14$, $s = 16$, $n = 9$, $\sqrt{n}=\sqrt{9}=3$, and $ME=\frac{2.14\times16}{3}=\frac{34.24}{3}\approx11.41$

Step5: Test the fourth option

For $z = 2.14$, $s = 16$, $n = 81$, $\sqrt{n}=\sqrt{81}=9$, and $ME=\frac{2.14\times16}{9}=\frac{34.24}{9}\approx3.80$

Answer:

$z = 2.14; s = 4; n = 81$