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

`MOE=\pm \ 1.41`

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) ((\sigma)/(√(n)))\\\\=\pm z_(0.025)*(\sigma)/(√(n))\\\\=\pm 1.96* (1.91)/(√(7))\\\\=\pm 1.41`

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