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

72 students will be accepted. (to find it you would divide 270 by 11 then multiply the product which is 24 by 3 and get 72)...

What is the minimum sample size required to estimate

scottytohotty

06.02.2022

The expression for the required minimum sample size is $n=[\frac{1.645\times\sigma }{D}]^{2}$ .

Step-by-step explanation:

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

$CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

$MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$

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:

$MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times\sigma }{MOE}]^{2}$

$n=[\frac{1.645\times\sigma }{D}]^{2}$

Thus, the expression for the required minimum sample size is $n=[\frac{1.645\times\sigma }{D}]^{2}$ .

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