Homework Help is Here – Start Your Trial Now!
Math
Statistics
ease solve below questions part 4 and 5.   Note:-Please don't mark this question as complex or unclear(image is clear please view in computer) and this is practice question zo don't mark as graded and someone already answered one part of this question on bartleby because I asked only 4 and 5 part

ease solve below questions part 4 and 5.   Note:-Please don't mark this question as complex or unclear(image is clear please view in computer) and this is practice question zo don't mark as graded and someone already answered one part of this question on bartleby because I asked only 4 and 5 part

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

Please solve below questions part 4 and 5.

 

Note:-Please don't mark this question as complex or unclear(image is clear please view in computer) and this is practice question zo don't mark as graded and someone already answered one part of this question on bartleby because I asked only 4 and 5 part 

Problem 2 Comparing two means Consider two measuring instruments that are used to measure the intensity of some electromagnetic waves. An engineer wants to check if both instruments are calibrated identically, i.e., if they will produce identical measurements for identical waves. To do so, the engineer does ni independent measurements of the intensity of a given wave using the first instrument, and n2 measurements on the same wave using the second instrument. The integers ni and n2 may not be equal because, for instance, one instrument may be more costly than the other one, or may produce measurements more slowly. The measurements are denoted by X1, . . ., Xn for the first instrument and by Y1, .. ., Ynz for the second one. Intrinsic defects of the instruments will lead to measurement errors, and it is reasonable to assume that X1, ..., Xn are iid Gaussian and so are Y1,..., Ynz: If the two instruments are identically calibrated, the X,'s and the Y,'s should have the same expectation but may not have the same variance, since the two instruments may not have the same precision. i.i.d. i.i.d. N(H1, o}) and Y1,..., Yna N(42, 03), Hence, we assume that X1, ..., Xn1 where u1, l2 ER and o?, o > 0, and that the two samples are independent of each other. We want to test whether u1 = l2. 2~ 1. Recall the expression of the maximum likelihood estimators for (u1, o?) and for (42, o). Denote these estimators by (@1, ô?) and (i2, 6). and of of 2. Recall the distribution of 3. What is the distribution of of 4. Let A = p - 2. What is the distribution of A ? 5. Consider the following hypotheses: Ho : "1 = 42" vs. Ho : "H1 = H2". Here and in the next question we assume that of o. Based on the previous questions, propose a test with non asymptotic level a E (0, 1) for Ho against H1. 6. Assume that 10 measurements have been done for both machines. The first in- strument measured 8.43 in average with sample variance 0.22 and the second in- strument measured 8.07 with sample variance 0.17. Can you conclude that the calibrations of the two machines are significantly identical at level 5% ? What is, approximately, the p-value of your test ?
Transcribed Image Text:Problem 2 Comparing two means Consider two measuring instruments that are used to measure the intensity of some electromagnetic waves. An engineer wants to check if both instruments are calibrated identically, i.e., if they will produce identical measurements for identical waves. To do so, the engineer does ni independent measurements of the intensity of a given wave using the first instrument, and n2 measurements on the same wave using the second instrument. The integers ni and n2 may not be equal because, for instance, one instrument may be more costly than the other one, or may produce measurements more slowly. The measurements are denoted by X1, . . ., Xn for the first instrument and by Y1, .. ., Ynz for the second one. Intrinsic defects of the instruments will lead to measurement errors, and it is reasonable to assume that X1, ..., Xn are iid Gaussian and so are Y1,..., Ynz: If the two instruments are identically calibrated, the X,'s and the Y,'s should have the same expectation but may not have the same variance, since the two instruments may not have the same precision. i.i.d. i.i.d. N(H1, o}) and Y1,..., Yna N(42, 03), Hence, we assume that X1, ..., Xn1 where u1, l2 ER and o?, o > 0, and that the two samples are independent of each other. We want to test whether u1 = l2. 2~ 1. Recall the expression of the maximum likelihood estimators for (u1, o?) and for (42, o). Denote these estimators by (@1, ô?) and (i2, 6). and of of 2. Recall the distribution of 3. What is the distribution of of 4. Let A = p - 2. What is the distribution of A ? 5. Consider the following hypotheses: Ho : "1 = 42" vs. Ho : "H1 = H2". Here and in the next question we assume that of o. Based on the previous questions, propose a test with non asymptotic level a E (0, 1) for Ho against H1. 6. Assume that 10 measurements have been done for both machines. The first in- strument measured 8.43 in average with sample variance 0.22 and the second in- strument measured 8.07 with sample variance 0.17. Can you conclude that the calibrations of the two machines are significantly identical at level 5% ? What is, approximately, the p-value of your test ?
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Complex Analysis
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.
Similar questions
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
SEE MORE TEXTBOOKS