Question

Ten samples of coal from a Northern Appalachian source had an average mercury content of 0.242 ppm with a standard deviation of 0.038 ppm. Find a 95% confidence interval for the mean mercury content of coal from this source. Round the answers to four decimal places.

The 95% confidence interval for the mean mercury content of coal from this source is

Answer 1

Solution :

Given that,

= 0.242

s =0.038

n = 10Degrees of freedom = df = n - 1 =10 - 1 = 9

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,9 = 2.262 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.262* (0.038 / 10)

= 0.0272

The 95% confidence interval estimate of the population mean is,

- E < < + E

0.242-0.0272 < < 0.242+ 0.0272

0.2148 < < 0.2692

( 0.2148 , 0.2692)