Question

Contaminated water: The concentration of benzene was measured in units of milligrams per liter for a simple random sample of five specimens of untreated wastewater produced at a gas field. The sample mean was 7.8 with a sample standard deviation of 3.1. Seven specimens of treated wastewater had an average benzene concentration of 3.7 with a standard deviation of 2.5. It is reasonable to assume that both samples come from populations that are approximately normal. Can you conclude that the mean benzene concentration is less in treated water than in untreated water? Let μ1 denote the mean benzene concentration in untreated wastewater.

Use the =α0.10 level and the critical value method with the table.

1. State the appropriate null and alternate hypotheses.
2. How many degrees of freedom are there, using the simple method?
3. Find the critical value(s). Round the answer to at least three decimal places. If there is more than one critical value, separate them with commas.
4. Compute the test statistic. Round the answer to at least three decimal places.
5.   Determine whether to reject H0
6. State a conclusion.

Answer 1

Can you conclude that the mean benzene concentration is less in treated water than in untreated water?

Let μ1 denote the mean benzene concentration in untreated wastewater.

Let μ2 denote the mean benzene concentration in treated wastewater.

We want to test that the, μ1 > μ2.

Sample 1: benzene concentration in untreated water

sample 2: benzene concentration in treated water

We may conclude that the data provide sufficient evidence to support claim that the mean benzene concentration is less in treated water than in untreated water.