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

The needed sample size is approximately 61.46 individuals.

Explanation:

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

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

Where
`S_d` is the standard deviation,
`{z_{1 - (\alpha)/(2)` is the quantile of the normal distribution with area of
`1 - (\alpha)/(2)` and
`e` is the acceptable error.

`n_0 = \big((1.96*20)/(5) \big) \approx 61.46`

We would need a sample size of 62 individuals.