Question

Which of the following z-values, standard deviations, and sample sizes produce a margin of error of 0. 95? M E = StartFraction z times s Over StartRoot n EndRoot EndFraction z = 2. 14; s = 4; n = 9 z = 2. 14; s = 4; n = 81 z = 2. 14; s = 16; n = 9 z = 2. 14; s = 16; n = 81.

Answer 1

The value of z-values, standard deviations, and sample sizes which produce a margin of error of 0.95 are 2.14, 4 and 81 respectively.

What is margin of error?

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error. The formula to calculate the margin of error is,

$MOE=z\times\dfrac{s}{\sqrt{n}}$

Here, (z) is z-values, (s) standard deviations, and (n) is sample size.

Which of the following z-values, standard deviations, and sample sizes produce a margin of error of 0. 95?

The values in the first option is given as z = 2. 14; s = 4; n = 9. Put these values in the above formula as,

$MOE=2.14\times\dfrac{4}{\sqrt{9}}\\MOE=2.85$

The values in the second option is given as z = 2. 14; s = 4; n = 81. Put these values in the above formula as,

$MOE=2.14\times\dfrac{4}{\sqrt{81}}\\MOE=0.95$

The values in the third option is given as z = 2. 14; s = 16; n = 9. Put these values in the above formula as,

$MOE=2.14\times\dfrac{16}{\sqrt{9}}\\MOE=11.41$

The values in the fourth option is given as z = 2. 14; s = 16; n = 81. Put these values in the above formula as,

$MOE=2.14\times\dfrac{16}{\sqrt{81}}\\MOE=3.80$

Hence, the value of z-values, standard deviations, and sample sizes which produce a margin of error of 0.95 are 2.14, 4 and 81 respectively.

Learn more about the margin of error here;

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