Question

A geologist examines 22 water samples for magnesium concentration. The mean magnesium concentration for the sample data is 0.637 cc/cubic meter with a standard deviation of 0.0358. Determine the 95% confidence interval for the population mean magnesium concentration. Assume the population is approximately normal.

Step 2 of 2 :

Construct the 95% confidence interval. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

=

s =0.0358

n = 22

Degrees of freedom = df = n - 1 = 22 - 1 = 21

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,21 = 2.080 ( using student t table)

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

= 2.080* (0.0358 / 22)

E= 0.016

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

- E < < + E

0.637- 0.016< < 0.637+ 0.016

0.621< < 0.653

( 0.621, 0.653 )