In: Statistics and Probability
The level of pesticides found in the blubber of whales is a measure of pollution of the oceans by runoff from land and can also be used to identify different populations of whales. A sample of six male minke whales in the West Greenland area of the North Atlantic found the mean concentration of the insecticide dieldrin to be x = 361 nanograms per gram of blubber (ng/g). Suppose that the concentration in all such whales varies Normally with population standard deviation σ = 57 ng/g.
Give a 95% confidence interval for estimating the mean level. (Round your answers to two decimal places.)
Solution:
Given:
Sample size = n = 6
Sample mean = nanograms per gram of blubber (ng/g)
the concentration in all such whales varies Normally with population standard deviation σ = 57 ng/g.
We have to find a 95% confidence interval for estimating the mean level.
Formula:
where
We need to find zc value for c=95% confidence level.
Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750
Look in z table for Area = 0.9750 or its closest area and find z value.
Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96
That is : Zc = 1.96
thus
thus