Let x be a random variable that represents micrograms of lead per liter of water (µg/L). An industrial plant discharges water into a creek. The Environmental Protection Agency (EPA) has studied the discharged water and found x to have a normal distribution, with σ = 0.7 µg/L. † Note: For degrees of freedom d.f. not in the Student's t table,use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) The industrial plant says that the population mean value of x is μ = 2.0 µg/L. However, a random sample of n = 10 water samples showed that x = 2.57 µg/L. Does this indicate that the lead concentration population mean is higher than the industrial plant claims? Use a = 1%. (i) What is the level of significance? What is the value of the sample test statistic? (Round your answer to two decimal places. (b) Find a 95% confidence interval for μ using the sample data and the EPA value for σ. (Round your answers to two decimal places.) lower limit µg/L upper limit µg/L (c) How large a sample should be taken to be 95% confident that the sample mean x is within a margin of error E = 0.2 µg/L of the population mean? (Round your answer up to the nearest whole number.) water samples
Let x be a random variable that represents micrograms of lead per liter of water (µg/L). An industrial plant discharges water into a creek. The Environmental Protection Agency (EPA) has studied the discharged water and found x to have a normal distribution, with σ = 0.7 µg/L. † Note: For degrees of freedom d.f. not in the Student's t table,use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) The industrial plant says that the population mean value of x is μ = 2.0 µg/L. However, a random sample of n = 10 water samples showed that x = 2.57 µg/L. Does this indicate that the lead concentration population mean is higher than the industrial plant claims? Use a = 1%. (i) What is the level of significance? What is the value of the sample test statistic? (Round your answer to two decimal places. (b) Find a 95% confidence interval for μ using the sample data and the EPA value for σ. (Round your answers to two decimal places.) lower limit µg/L upper limit µg/L (c) How large a sample should be taken to be 95% confident that the sample mean x is within a margin of error E = 0.2 µg/L of the population mean? (Round your answer up to the nearest whole number.) water samples
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Let x be a random variable that represents micrograms of lead per liter of water (µg/L). An industrial plant discharges water into a creek. The Environmental Protection Agency (EPA) has studied the discharged water and found x to have a
σ = 0.7 µg/L.
† Note: For degrees of freedom d.f. not in the Student's t table,use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer.
(a) The industrial plant says that the population mean value of x is
μ = 2.0 µg/L.
However, a random sample of
n = 10
water samples showed that
x = 2.57 µg/L.
Does this indicate that the lead concentration population mean is higher than the industrial plant claims? Use
a = 1%.
(i) What is the level of significance?
What is the value of the sample test statistic? (Round your answer to two decimal places.
(b) Find a 95% confidence interval for μ using the sample data and the EPA value for σ. (Round your answers to two decimal places.)
(c) How large a sample should be taken to be 95% confident that the sample mean
water samples
lower limit | µg/L |
upper limit | µg/L |
(c) How large a sample should be taken to be 95% confident that the sample mean
x
is within a margin of error
E = 0.2 µg/L
of the population mean? (Round your answer up to the nearest whole number.) water samples
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 9 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman