Question

Find the sample size required to achieve the given margin of error with SD = 51.02 and z - score = 1.96. Round your answer to the nearest whole number. margin of error = 2

Answer 1

Answer:

The sample size required is 2500.

Step-by-step explanation:

z-score:

In function of the margin of error M, the z-score is given by:

$Z = \frac{M}{\frac{\sigma}{\sqrt{n}}} = \frac{M\sqrt{n}}{\sigma}$

In this question, we have that:

$\sigma = 51.02, M = 2, Z = 1.96$

So

$Z = \frac{M\sqrt{n}}{\sigma}$

$1.96 = \frac{2\sqrt{n}}{51.02}$

$2\sqrt{n} = 51.02*1.96$

$\sqrt{n} = \frac{51.02*1.96}{2}$

$(\sqrt{n})^2 = (\frac{51.02*1.96}{2})^2$

$n = 2500$

The sample size required is 2500.