Question

If the estimated population standard deviation based on previous studies is 20 percent, the acceptable error is plus or minus 5 percent, and the z-value for a 95 percent level of confidence is 1.96, the needed sample size is approximately:__________________

Answer 1

Answer:

The needed sample size is approximately 61.46 individuals.

Step-by-step explanation:

We can use the following formula to obtain the sample size:

$n_0 = \big(\frac{z_{1 - \frac{\alpha}{2}}S_d}{e} \big)$

Where $S_d$ is the standard deviation, ${z_{1 - \frac{\alpha}{2}$ is the quantile of the normal distribution with area of $1 - \frac{\alpha}{2}$ and $e$ is the acceptable error.

$n_0 = \big(\frac{1.96\times20}{5} \big) \approx 61.46$

We would need a sample size of 62 individuals.