Fifteen (15) samples of water were collected from a certain treatment facility in order to gain some insight regarding the amount of coliform in the urban pipeline. The concentration of the coliform is measured in parts per million (ppm), per liter. Suppose that the mean at the treatment facility is not as important as the upper extreme of the distribution of the amount of coliform detected. The concern is whether the concentration of coliform is too large. Readings for the 15 water samples gave a sample mean of 3.84 ppm p liter and a standard deviation of 3.07 ppm per liter. Assume that the readings are a random sample from a normal distribution.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

2

Fifteen (15) samples of water were collected from a certain treatment facility in order to gain some insight regarding the amount of
coliform in the urban pipeline. The concentration of the coliform is measured in parts per million (ppm), per liter. Suppose that the
mean at the treatment facility is not as important as the upper extreme of the distribution of the amount of coliform detected. The
concern is whether the concentration of coliform is too large. Readings for the 15 water samples gave a sample mean of 3.84 ppm per
liter and a standard deviation of 3.07 ppm per liter. Assume that the readings are a random sample from a normal distribution.
Calculate a Prediction Interval (upper 95% prediction limit) and a Tolerance Limit (95% upper tolerance limit that exceeds 95% of the
population values). Interpret both; that is, tell what each communicates about the upper extreme of the distribution of coliform at the
sampling in the treatment facility.
O a. Prediction Upper Limit: Xp+1<10.597. This means that a new observation will have a chance of 95% to fall below the upper limit.
Tolerance Upper Limit: 11.72. Hence, we are 95% confident that a limit of 11.72 will contain 95% of the coliform measurement in the water
samples
Ob.Prediction Upper Limit: Xn+1<9.398. This means that a new observation will have a chance of 95% to fall below the upper limit. Tolerance
Upper Limit: 11.86. Hence, we are 95% confident that a limit of 11.86 will contain 95% of the coliform measurement in the water samples
O C. Prediction Upper Limit: Xn+1< 10.641. This means that a new observation will have a chance of 95% to fall below the upper limit.
Tolerance Upper Limit: 12.91. Hence, we are 95% confident that a limit of 12.91 will contain 95% of the coliform measurement in the water
samples
O d. Prediction Upper Limit: Xn+1<9.424. This means that a new observation will have a chance of 95% to fall below the upper limit. Tolerance
Upper Limit: 11.72. Hence, we are 95% confident that a limit of 11.72 will contain 95% of the coliform measurement in the water samples
Transcribed Image Text:Fifteen (15) samples of water were collected from a certain treatment facility in order to gain some insight regarding the amount of coliform in the urban pipeline. The concentration of the coliform is measured in parts per million (ppm), per liter. Suppose that the mean at the treatment facility is not as important as the upper extreme of the distribution of the amount of coliform detected. The concern is whether the concentration of coliform is too large. Readings for the 15 water samples gave a sample mean of 3.84 ppm per liter and a standard deviation of 3.07 ppm per liter. Assume that the readings are a random sample from a normal distribution. Calculate a Prediction Interval (upper 95% prediction limit) and a Tolerance Limit (95% upper tolerance limit that exceeds 95% of the population values). Interpret both; that is, tell what each communicates about the upper extreme of the distribution of coliform at the sampling in the treatment facility. O a. Prediction Upper Limit: Xp+1<10.597. This means that a new observation will have a chance of 95% to fall below the upper limit. Tolerance Upper Limit: 11.72. Hence, we are 95% confident that a limit of 11.72 will contain 95% of the coliform measurement in the water samples Ob.Prediction Upper Limit: Xn+1<9.398. This means that a new observation will have a chance of 95% to fall below the upper limit. Tolerance Upper Limit: 11.86. Hence, we are 95% confident that a limit of 11.86 will contain 95% of the coliform measurement in the water samples O C. Prediction Upper Limit: Xn+1< 10.641. This means that a new observation will have a chance of 95% to fall below the upper limit. Tolerance Upper Limit: 12.91. Hence, we are 95% confident that a limit of 12.91 will contain 95% of the coliform measurement in the water samples O d. Prediction Upper Limit: Xn+1<9.424. This means that a new observation will have a chance of 95% to fall below the upper limit. Tolerance Upper Limit: 11.72. Hence, we are 95% confident that a limit of 11.72 will contain 95% of the coliform measurement in the water samples
Expert Solution
steps

Step by step

Solved in 2 steps with 5 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman