Using technology, solve the following problem: The concentration of hexane (a common solvent) was measured in units of micrograms per liter for a simple random sample of fourteen specimens of
Untreated ground water taken near a municipal landfill. The sample mean was 241.8 with a sample Standard deviation of 8.8. Ten specimens of treated ground water had an average hexane Concentration of 149.5 with a standard deviation of 7.4.
It is reasonable to assume that both samples come from populations that are approximately normal. Construct A 95% confidence interval for the reduction of hexane concentration after treatment.
A) (9.242, 9.960)
B) (85.407, 99.193)
C) (86.595, 98.005)
D) (9.306, 9.900)

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the difference in means (untreated - treated), we use the formula for the confidence interval of the difference between two means for independent samples. The formula incorporates the sample means, sample standard deviations, and sample sizes of the two groups. Given the data:- Mean of untreated ground water = 241.8- Standard deviation of untreated ground water = 8.8- Sample size of untreated ground water = 14- Mean of treated ground water = 149.5- Standard deviation of treated ground water = 7.4- Sample size of treated ground water = 10The confidence interval is calculated using the formula for the difference between two independent means with unknown but assumed equal variances. The calculation involves finding the standard error of the difference between the two means, then using the t-distribution to find the critical value for the 95% confidence level, and finally calculating the interval.The correct interval, given the calculations, is (85.407, 99.193), which represents the estimated range of reduction in hexane concentration due to treatment with 95% confidence. This interval suggests that, on average, the treatment reduces the hexane concentration by between 85.407 and 99.193 micrograms per liter.

Using Technology, Solve the Following Problem: the Concentration of Hexane