1. A random sample of n = 20 products are taken from the production lines of a factory. Let = 1,..., 20, IID Xi Bernoulli (p) be the indicator of whether the i-th product defective for i where Р denotes the proportion of defective products in the population. It is desirable to test whether the the proportion of defective products is below 30%. (a) State the null hypothesis Ho and the alternative hypothesis Ha. (b) Describe the events of Type I error and Type II error in the procedure of making statistical decisions. = (c) Let T ₁X₁ denote the number of defective items in the sample. Suppose that we decide to reject Ho if T ≤ 4. Let (p) denote the corresponding power function, i.e., T(p) = Pr (T ≤ 4|p). ine he value of (p) at the points p = 0, 0.1, 0.2, 0.3,...,0.9, and 1.0 and etch the power function. (Hint: Use the statistical table for Binomial distribution.) (d) What is the size of the test procedure in part (c), i.e., the maximum probability of making Type I error? (e) What is the power of the test procedure in part (c) when p = 0.1? (Hint: Both part (d) and part (e) can be obtained immediately from the power function (p).)
1. A random sample of n = 20 products are taken from the production lines of a factory. Let = 1,..., 20, IID Xi Bernoulli (p) be the indicator of whether the i-th product defective for i where Р denotes the proportion of defective products in the population. It is desirable to test whether the the proportion of defective products is below 30%. (a) State the null hypothesis Ho and the alternative hypothesis Ha. (b) Describe the events of Type I error and Type II error in the procedure of making statistical decisions. = (c) Let T ₁X₁ denote the number of defective items in the sample. Suppose that we decide to reject Ho if T ≤ 4. Let (p) denote the corresponding power function, i.e., T(p) = Pr (T ≤ 4|p). ine he value of (p) at the points p = 0, 0.1, 0.2, 0.3,...,0.9, and 1.0 and etch the power function. (Hint: Use the statistical table for Binomial distribution.) (d) What is the size of the test procedure in part (c), i.e., the maximum probability of making Type I error? (e) What is the power of the test procedure in part (c) when p = 0.1? (Hint: Both part (d) and part (e) can be obtained immediately from the power function (p).)
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
Just E please
Transcribed Image Text:1. A random sample of n = 20 products are taken from the production lines of a factory. Let
IID
Xi Bernoulli(p) be the indicator of whether the i-th product defective for i = 1,..., 20,
where р denotes the proportion of defective products in the population. It is desirable to test
whether the the proportion of defective products is below 30%.
(a) State the null hypothesis Ho and the alternative hypothesis Ha.
(b) Describe the events of Type I error and Type II error in the procedure of making statistical
decisions.
20
i=1
(c) Let T = 2₁X; denote the number of defective items in the sample. Suppose that we
Σ
decide to reject Ho if T ≤ 4. Let (p) denote the corresponding power function, i.e.,
T(P) = Pr (T≤4|p).
Determine the value of (p) at the points p = 0, 0.1, 0.2, 0.3,...,0.9, and 1.0 and sketch
the power function. (Hint: Use the statistical table for Binomial distribution.)
(d) What is the size of the test procedure in part (c), i.e., the maximum probability of making
Type I error?
(e) What is the power of the test procedure in part (c) when p = 0.1? (Hint: Both part (d)
and part (e) can be obtained immediately from the power function (p).)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
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