Question

Treatment of wastewater is important to reduce the concentration of undesirable pollutants. One such substance is benzene which used as industrial solvent. Two methods of water treatment are being compared. Treatment 1 is applied to 5 specimens of wastewater while Treatment 2 is applied to 7 specimens. The benzene concentrations in milligrams per liter are as follows:

Treatment 1	Treatment 2
x1-bar: 6.8 mg/L	x2-bar: 5.7 mg/L
s1: 0.9 mg/L	s2: 1.6 mg/L
n1: 5	n2: 7

State the conclusion addressing the original claim, in context.

Answer 1

Let X: The benzene concentrations in milligrams per liter for treatment 1

Y:The benzene concentrations in milligrams per liter for treatment 2

assuming that each observation of the data is sample from normal distribution we go as follows

So here we need to compare between the two treatments.Hence the hypothesis are

The construction of the test statistic is as follows

The value of the test statistic under H0 is

The p-value is

So at 5% level of significance we see that the p-value >0.05.So we conclude that there is enough evidence to accept H0 so we can say there is no significant difference in mean of the benzene concentrations in milligrams per liter for treatment 1 and treatment 2.