Answered: People suffering from hypertension,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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8. An application of the distribution of sample means

People 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 Distribution

Mean = 19.5

Standard 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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