Question

A biologist examines 23 sedimentary samples for bromide concentration. The mean bromide concentration for the sample data is 0.349 cc/cubic meter with a standard deviation of 0.0527. Determine the 98%

confidence interval for the population mean bromide 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.

Answer 1

Solution :

Given that,

= 0.349

s =0.0527

n =23 Degrees of freedom = df = n - 1 =23 - 1 = 22

At 98% confidence level the t is

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

t /2,df = t0.01,22 =2.508 ( using student t table)

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

= 2.508 * (0.0527 / 23)

= 0.0276

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

- E < < + E

0.349 - 0.0276< <0.349 + 0.0276

0.3214 < < 0.3766

( 0.3214 , 0.3766)