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 3.7 with a sample standard deviation of 1.8. Seven specimens of treated wastewater had an average benzene concentration of 7.2 with a standard deviation of 3. It is reasonable to assume that both samples come from populations that are approximately normal. Can you conclude that the mean benzene concentration is more in treated water than in untreated water? Let μ1denote the mean benzene concentration for untreated water and μ2 denote the mean benzene concentration for treated water. Use the a=0.01level the P-value method with the TI-84 Plus calculator.

find p-value:

Answer 1

The null and alternate hypothesis:

Level of significance

Test statistic:

where is the pooled variance of the samples.

The critical region for this left sided test is

, the p-value is 0.0218. The p-value is >0.01.

Since it is observed that    the null hypothesis is not rejected. Hence we conclude that there is not enough evidence to claim that the ​ the mean benzene concentration is more in treated water than in untreated water.