Question

Assuming that the samples come from normal distribution, find the margin of error E given the following:

n = 10 and x̄ = 28 with s = 4.0, 90% confidence

Answer 1

n=10, $\bar{x}$ =28, s=4, $\alpha$ =100-90=10%=0.1

$Z_{\frac{\alpha}{2}}=Z_{0.05}=2.575$

Therefore, The critical value is 2.575.

The standard deviation is 2.0, but as this is a sample, we need the standard error for the mean.

 

The formula for the SE of the mean $\sigma= \dfrac{s}{\sqrt{n}}$ ,

so: $\sigma=\dfrac{2}{\sqrt{10}}=0.6325.$

Margin of Error=$2.575 \times 0.6325 = 1.629.$

Therefore, the margin of error is 1.629.