Chapter 7, Problem T7.6SPT

To determine

To find: the sample size should be used by researcher.

Answer to Problem T7.6SPT

640

Explanation of Solution

Calculation:

The original sample size is 160

  ${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}$

To making the standard deviation half as big

  $\frac{{\sigma }_{\overline{x}}}{2}=\frac{1}{2}\times \frac{\sigma }{\sqrt{n}}=\frac{\sigma }{2\sqrt{n}}=\frac{\sigma }{\sqrt{2^{2}n}}=\frac{\sigma }{\sqrt{4n}}$

It is observed that the sample size $n$ is replaced by $4n$ in the equation of the standard deviation, which means that the sample quadruples in size. The original sample size $n$ was 160. The sample with half as big a standard deviation is:

  $4n=4\left(160\right)=640$

Hence, the correct option is (d)