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.

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

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 How to Enter) 2 Points 圆Keypad

Answer 1

Solution:

Given,

n = 6 (sample size)

= 0.714

s = 0.0126

c = 90% = 0.90

Since population sd is not given, we use t distribution.

Formula for confidence interval for mean is

= 1 - c = 1 - 0.90 = 0.10

so, /2 = 0.05

Also ,n = 6 implies d.f.=n - 1= 5

so critical value used in the confidence interval is

ta/2,d.f
=
ta/2,n-1
= t _0.05,5 = 2.015 (using t table)

So required confidence interval is

0.714 - 2.015*(0.0126/ 6) 0.714 + 2.015*(0.0126/ 6)

(0.7036 , 0.724) is the required interval.