Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is D

Answer 1

The expression for the required minimum sample size is
`n=[(1.645*\sigma )/(D)]^(2)`.

Explanation:

The (1 - α) % confidence interval for population mean is:

`CI=\bar x\pm z_(\alpha/2)\cdot(\sigma)/(√(n))`

The margin of error for this interval is:

`MOE=z_(\alpha/2)\cdot(\sigma)/(√(n))`

Confidence level = 90%

α = 10%

Compute the critical value of z for α = 10% as follows:

z = 1.645

*Use a z-table.

Compute the sample size required as follows:

`MOE=z_(\alpha/2)\cdot(\sigma)/(√(n))`

`n=[(z_(\alpha/2)*\sigma )/(MOE)]^(2)`

`n=[(1.645*\sigma )/(D)]^(2)`

Thus, the expression for the required minimum sample size is
`n=[(1.645*\sigma )/(D)]^(2)`.