Question

A geologist examines 18 water samples for iron concentration. The mean iron concentration for the sample data is 0.272 cc/cubic meter with a standard deviation of 0.08510 Determine the 99% confidence interval for the population mean iron concentration. Assume the population is approximately normal.

Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 2: Construct the 99% confidence interval. Round your answer to three decimal places.

Answer 1

Solution :

degrees of freedom = n - 1 = 18 - 1 = 17

t/2,df = t0.005,17 = 2.898

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

= 2.898 * ( 0.08510/ 18)

Margin of error = E = 0.058

The 99% confidence interval estimate of the population mean is,

  ± E  

= 0.272 ± 0.058

= ( 0.214, 0.330 )