8. An application of the distribution of sample meansPeople suffering from hypertension, heart disease, or kidney problems may need to limit their intakes of sodium. The public health departments in some US states and Canadian provinces require community water systems to notify their customers if the sodium concentration in the drinking water exceeds a designated limit. In Ontario, for example, the notification level is 20 mg/L (milligrams per liter).Suppose that over the course of a particular year the mean concentration of sodium in the drinking water of a water system in Ontario is 18.3 mg/L, and the standard deviation is 6 mg/L.Imagine that the water department selects a simple random sample of 31 water specimens over the course of this year. Each specimen is sent to a lab for testing, and at the end of the year the water department computes the mean concentration across the 31 specimens. If the mean exceeds 20 mg/L, the water department notifies the public and recommends that people who are on sodium-restricted diets inform their physicians of the sodium content in their drinking water.Use the Distributions tool to answer the following question. (Hint: Start by setting the mean and standard deviation parameters on the tool to the expected mean and standard error for the distribution of sample mean concentrations.) Normal DistributionMean = 19.5Standard Deviation = 0.85 10.012.014.016.018.020.022.024.0Mz-11.0-9.0-7.0-5.0-3.0-1.01.03.05.0z Even though the actual concentration of sodium in the drinking water is within the limit, there is a probability that the water department will erroneously advise its customers of an above-limit concentration of sodium. Suppose that the water department wants to reduce its risk of erroneously notifying its customers that the sodium concentration is above the limit. Assuming the water department can’t change the mean or the standard deviation of the sodium concentration in the drinking water, is there anything the department can do to reduce the risk of notifying its customers that the sodium concentration is above the limit when it actually is not?No, there is nothing it can do. It can collect fewer specimens over the course of the year. It can collect more specimens over the course of the year.

Question

8. An application of the distribution of sample meansPeople suffering from hypertension, heart disease, or kidney problems may need to limit their intakes of sodium. The public health departments in some US states and Canadian provinces require community water systems to notify their customers if the sodium concentration in the drinking water exceeds a designated limit. In Ontario, for example, the notification level is 20 mg/L (milligrams per liter).Suppose that over the course of a particular year the mean concentration of sodium in the drinking water of a water system in Ontario is 18.3 mg/L, and the standard deviation is 6 mg/L.Imagine that the water department selects a simple random sample of 31 water specimens over the course of this year. Each specimen is sent to a lab for testing, and at the end of the year the water department computes the mean concentration across the 31 specimens. If the mean exceeds 20 mg/L, the water department notifies the public and recommends that people who are on sodium-restricted diets inform their physicians of the sodium content in their drinking water.Use the Distributions tool to answer the following question. (Hint: Start by setting the mean and standard deviation parameters on the tool to the expected mean and standard error for the distribution of sample mean concentrations.) Normal DistributionMean = 19.5Standard Deviation = 0.85    10.012.014.016.018.020.022.024.0Mz-11.0-9.0-7.0-5.0-3.0-1.01.03.05.0z Even though the actual concentration of sodium in the drinking water is within the limit, there is a    probability that the water department will erroneously advise its customers of an above-limit concentration of sodium. Suppose that the water department wants to reduce its risk of erroneously notifying its customers that the sodium concentration is above the limit. Assuming the water department can’t change the mean or the standard deviation of the sodium concentration in the drinking water, is there anything the department can do to reduce the risk of notifying its customers that the sodium concentration is above the limit when it actually is not?No, there is nothing it can do. It can collect fewer specimens over the course of the year. It can collect more specimens over the course of the year.

Accepted Answer

Answered: Image /qna-images/answer/ba202452-f9e1-4928-994a-0682a3d4adad.jpg