Question

Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain." The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviationσ= 0.5. A sample ofndays finds that the mean pH isx= 4.8. Give a 99 % confidence interval for the mean pH μ when n = 5, n = 15, and n = 40. n= 5 to n = 15 to n = 40 to

Answer 1

Solution:

We are given:

is the critical value at 0.01 significance level

The 99% confidence interval for the mean pH when n = 5 is:

The 99% confidence interval for the mean pH when n = 15 is:

The 99% confidence interval for the mean pH when n = 40 is: