91影视

The confidence interval is 90%.

The sample standard deviation is 20%.

The sampling error is 5%.

The general formula for the sample size is given below

$n={\left[\frac{Z_{\frac{伪}{2}}\left(蟽\right)}{SE}\right]}^2$

Where SE represents the sampling error.

The value of$蟽$is usually unknown. It can be estimated by the standard deviation, s from the prior sample.

For the confidence level of 90%, the level of significance is 0.90

$$\begin{gathered} For\left(1-伪\right)=0.90 \\ 伪=0.10 \\ \frac{伪}{2}=0.05 \end{gathered}$$

The$Z_{\frac{伪}{2}}$corresponding to the standard normal table is:

$$\begin{gathered} Z_{\frac{伪}{2}}=Z_{0.05} \\ =1.645 \end{gathered}$$

The sample standard deviation is,

$$\begin{gathered} s=\frac{20}{100} \\ =0.2 \end{gathered}$$

The sampling error is,

$$\begin{gathered} SE=\frac{5}{100} \\ =0.05 \end{gathered}$$

The sample size is computed as:

$$\begin{gathered} n={\left[\frac{\left(1.645\right)\left(0.2\right)}{0.05}\right]}^2 \\ ={\left[6.58\right]}^2 \\ =43.2964 \\ 鈮�43 \end{gathered}$$

Hence, the number of swimming pools must be sampled to estimate the actual mean absolute deviation percentage to within 5% using a 90% confidence interval is 43.