Question

In a lake pollution study, the concentration of lead in the upper sedimentary layer of a lake bottom is measured from 25 sediment samples of 1000 cubic centimeters each. The sample mean and the sample standard deviation of the measurements are found to be .38 and 0.06, respectively.

(a) Compute a 99% confidence interval for the mean concentration of lead per 1000 cubic centimeters of sediment in the lake bottom.

(b) State any assumption in (a) that is needed about the population distribution.

Answer 1

Let X be the concentration of lead in the upper sedimentary layer of a lake bottom.

Given n=25

a) The 99% confidence interval for the mean concentration of lead per 1000 cubic centimeters of sediment in the lake bottom given by:

Hence The 99% confidence interval for the mean concentration of lead per 1000 cubic centimeters of sediment in the lake bottom is

b) The assumption we required is: Population needs to be approximately normally distributed.