6 6 The concentration of benzene was measured in units of mi

6.

6. The concentration of benzene was measured in units of milligrams per Liter for a simple random sample of seven specimens of untreated wastewater produced at a gas field. The sample mean was 7.7 with a sample standard deviation of 1.3. Nine specimens of treated wastewater had an average benzene concentration of 3.5 with a standard deviation of 1.5. It is reasonable to assume that both samples come from populations that are approximately normal. Construct a 95% confidence interval for the reduction in benzene concentration after treatment. Round the answer to one decimal place. A 95% confidence interval for the reduction in benzene concentration after treatment is

Solution

The degree of freedom =n1+n2-2=7+9-2 =14

Given a=0.05, t(0.025, df=14) =2.14 (from student t table)

So the lower bound is

(xbar1-xbar2) - t*sqrt(s1^2/n1+s2^2/n2)

=(7.7-3.5)-2.14*sqrt(1.3^2/7+1.5^2/9)

=2.7

So the upper bound is

(xbar1-xbar2) + t*sqrt(s1^2/n1+s2^2/n2)

=(7.7-3.5) + 2.14*sqrt(1.3^2/7+1.5^2/9)

=5.7