Question

A biologist examines 6 geological samples for lead concentration. The mean lead concentration for the sample data is 0.714 cc/cubic meter with a standard deviation of 0.0126. Determine the 90% confidence interval for the population mean lead concentration. Assume the population is approximately normal. Step 2 of 2: Construct the 90% confidence interval. Round your answer to three decimal places.

Answer 1

Given that,

= 0.714

s =0.0126

n = 6

Degrees of freedom = df = n - 1 = 6- 1 =5

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,5 = 2.015    ( using student t table)

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

= 2.015* (0.0126 / 6) = 0.010

The 90% confidence interval estimate of the population mean is,

- E < < + E

0.714- 0.010 < <0.714 + 0.010

0.704< < 0.724

( 0.704, 0.724)