Question

In monitoring lead in the air after the explosion at the battery factory, it is found that the amounts of lead over a 7 day period had a standard error of 1.91. Find the margin of error that corresponds to a 95% confidence interval. (Round to 2 decimal places)

Answer 1

Answer:

$MOE=\pm \ 1.41$

Step-by-step explanation:

-Given that $\sigma=1.91, n=7$

-We determine the z-value corresponding to the 95% confidence level:

$z_{\alpha/2}=z_{0.025}=1.96$

-The margin of error is the degree of error from the real value and is calculated as follows:

$MOE=\pm z_{\alpha/2} (\frac{\sigma}{\sqrt{n}})\\\\=\pm z_{0.025}\times\frac{\sigma}{\sqrt{n}}\\\\=\pm 1.96\times \frac{1.91}{\sqrt{7}}\\\\=\pm 1.41$

Hence, the margin of error is $\pm 1.41$