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 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

Given that,

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 mean is,

- E < < + E

0.714 - 0.010 < <0.714 + 0.010

0.704 < < 0.724

( 0.704 , 0.724)

The 90% confidence interval estimate of the mean is,( 0.704 , 0.724)