People suffering from hypertension, heart disease, or kidney problems may need t

Question

People suffering from hypertension, heart disease, or kidney problems may need to limit their intakes of sodiurm. The public health departments in some U.S. states and Canadian provinces require community water systems to notify their austomers if the sodium concentration in the drinking water exceeds a designated limit. In Ontario, for example, the notification level is 20 mg/L (mi ligrams 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 mg/, and the standard deviation is 6 mg/l. Imagine that the water department selects a simple random sample of 30 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 30 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 Distribution Mean 19.5 Standard Deviation 0.85 10 12 14 16 18 20 24 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

Explanation / Answer

Answer : It can collect more specimens over the course of the year.

Explanation: The probability of making an error depends on how large is the spread of the sampling distribution of sample mean is. Spread of the sampling distribution is measured in terms of standard deviation and is given by SD / sqrt(N) ; where SD is the std deviation of the orignial sodium concentration in water is and N is the sample size. So if we collect more sample we have higher N and therefore lower spread ans hence lower probabilty(risk) of making error.

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