Question

Eight specimens of untreated wastewater produced at a gas field had an average benzene concentration of 6.83 mg/L with a standard deviation of 1.72 mg/L. Seven specimens of treated waste water had an average benzene concentration of 3.32 mg/L with a standard deviation of 1.17 mg/L. Let μX represent the population mean for untreated wastewater and let μY represent the population mean for treated wastewater. Find a 95% confidence interval for the difference μX−μY . Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

The 95% confidence interval is ( , ).

Answer 1

Let X and Y represents the specimen of untreated and treated wastewater produced at a gas field. Then in case of untreated wastewater, we have average concentration of 6.83mg/L and standard deviation of 1.72mg/L. Then in case of treated wastewater, we have average benzene concentration of 3.32mg/L and standard deviation of 1.17mg/L.

Then

    

Let us consider a null hypothesis and alternative hypothesis as

The confidence interval for given level of significance is  is given by

There are 8 specimen of untreated wate water and 7 specimen of treated waste water. Then

For 95% confidence interval we have (100-95)%=5% level of significance. Therefore, we have

Here t value is calculated using the table of t distribution with 13 degree of freedom

The required confidence interval is (2.3920, 4.6279).