Trihalomethanes (or THM’s) refers to a broad class of organic compounds, including chloroform and bromoform. Many THM’s are known or suspected human carcinogens, and, because they are a biproduct of disinfection in water treatment facilities, their concentrations in drinking water are regulated by federal law. Four measurements of THM levels in drinking water yielded the following results, in parts per billion (ppb): 48, 65, 72, and 70. Assume that we know, from other drinking water quality surveys, that THM concentrations of this magnitude tend to be roughly normally distributed.(a) What is the mean THM concentration for this sample of four measurements?(b) What is the standard deviation of the sample and what is the standard error of the mean?(c) What is the 95% (two-tailed) confidence interval for the mean?(d) What is the 95% prediction interval for the individual measurements? That is, what interval encloses 95%of all possible data, given the mean and standard deviation that you have calculated?

Question

Trihalomethanes (or THM’s) refers to a broad class of organic compounds, including chloroform and bromoform. Many THM’s are known or suspected human carcinogens, and, because they are a biproduct of disinfection in water treatment facilities, their concentrations in drinking water are regulated by federal law. Four measurements of THM levels in drinking water yielded the following results, in parts per billion (ppb): 48, 65, 72, and 70. Assume that we know, from other drinking water quality surveys, that THM concentrations of this magnitude tend to be roughly normally distributed.(a)  What is the mean THM concentration for this sample of four measurements?(b)  What is the standard deviation of the sample and what is the standard error of the mean?(c)  What is the 95% (two-tailed) confidence interval for the mean?(d)  What is the 95% prediction interval for the individual measurements? That is, what interval encloses 95%of all possible data, given the mean and standard deviation that you have calculated?

Nico Buck · Accepted Answer

Given that,Four measurements of THM levels in drinking water yielded the following results, in parts per billion (ppb): 48, 65, 72, and 70.(a) Mean THM concentration for this sample of four measurements:The mean can be calculated using EXCEL function &quot;=AVERAGE (select array of data values)&quot; as follows:Thus, the mean THM concentration for this sample of four measurements is 63.75.(b) Standard deviation for this sample of four measurements:The standard deviation can be calculated using EXCEL function &quot;=STDEV (select array of data values)&quot; as follows:Thus, the standard deviation for this sample of four measurements is 10.905.Standard error:The standard error can be calculated as given below:SE=(sn)=10.9054=5.453

Naima Silva · Accepted Answer

(c) 95% (two-tailed) confidence interval for the mean:Critical value:The two tailed t critical value at 3 degrees of freedom and 95% confidence level is 3.1824.Calculation:The 95% (two-tailed) confidence interval for the mean can be calculated as follows:Cl=x―±(tc×SE)=63.75±(3.1824×5.453)=63.75±17.354=(46.396,81.104)Thus, the 95% (two-tailed) confidence interval for the mean is (46.396,81.104).

Trihalomethanes (or THM’s) refers to a broad class

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