Question

A physicist examines 28 sedimentary samples for mercury concentration. The mean mercury concentration for the sample data is 0.863 cc/cubic meter with a standard deviation of 0.0036

Determine the 98% confidence interval for the population mean mercury concentration. Assume the population is approximately normal.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 0.863

Population standard deviation =    = 0.0036

Sample size = n = 28

At 98% confidence level

= 1 - 98%  

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = Z_0.01 = 2.326

Margin of error = E = Z/2 * ( /n)

= 2.326 * ( 0.0036 /  28 )

= 0.002

At 98% confidence interval estimate of the population mean is,

- E < < + E

0.863 - 0.002 <   < 0.863 + 0.002

0.861 <   < 0.865

( 0.861 , 0.865 )

The 98% confidence interval for the population mean : ( 0.861 , 0.865 )