12. (MINITAB doesn't support this method. See Chapter 8 in the DOE book.) An experiment is required to estimate the slope of response y as a linear function of independent variable x, i.e. the model for y(x) has the form = yi bo+ bị Xi+€i where the b; are regression coefficients that estimate the ß; parameters. The safe range of x values is limited to the interval 20 ≤ x ≤40. The nominal slope is expected to be ẞ₁ = dy/dx = 6 and the experiment must estimate the true slope with 10% precision and 95% confidence, i.e. the 95% confidence interval for the slope parameter B₁ should have the form P(b₁-8
12. (MINITAB doesn't support this method. See Chapter 8 in the DOE book.) An experiment is required to estimate the slope of response y as a linear function of independent variable x, i.e. the model for y(x) has the form = yi bo+ bị Xi+€i where the b; are regression coefficients that estimate the ß; parameters. The safe range of x values is limited to the interval 20 ≤ x ≤40. The nominal slope is expected to be ẞ₁ = dy/dx = 6 and the experiment must estimate the true slope with 10% precision and 95% confidence, i.e. the 95% confidence interval for the slope parameter B₁ should have the form P(b₁-8
Chapter3: Polynomial Functions
Section: Chapter Questions
Problem 18T
Related questions
Question
Answer
(a) N = 64
(b) N = 192
(c) N = 96
Posting same question 4th time. Solve correct way
![12. (MINITAB doesn't support this method. See Chapter 8 in the DOE book.) An experiment is required to
estimate the slope of response y as a linear function of independent variable x, i.e. the model for y(x)
has the form
=
yi bo+ bị Xi+€i
where the b; are regression coefficients that estimate the ß; parameters. The safe range of x values is
limited to the interval 20 ≤ x ≤40. The nominal slope is expected to be ẞ₁ = dy/dx = 6 and the
experiment must estimate the true slope with 10% precision and 95% confidence, i.e. the 95%
confidence interval for the slope parameter B₁ should have the form
P(b₁-8<B₁ <b₁ + 8) = 0.95
where S = 0.6. The standard deviation of the noise is expected to be σ = 24. Determine the total
number of observations required under each of the following experiment designs:
a. All of the observations are concentrated at the two extreme levels of x in a balanced manner.
b. Observations are distributed uniformly between 20 and 40.
c. An equal number of observations are taken at each of x =
20, 30, and 40.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7559a47-bb34-494d-9e33-22c98791555e%2F895cd155-d705-48cc-a0ac-2c531d85ffd7%2Fayfq8fv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12. (MINITAB doesn't support this method. See Chapter 8 in the DOE book.) An experiment is required to
estimate the slope of response y as a linear function of independent variable x, i.e. the model for y(x)
has the form
=
yi bo+ bị Xi+€i
where the b; are regression coefficients that estimate the ß; parameters. The safe range of x values is
limited to the interval 20 ≤ x ≤40. The nominal slope is expected to be ẞ₁ = dy/dx = 6 and the
experiment must estimate the true slope with 10% precision and 95% confidence, i.e. the 95%
confidence interval for the slope parameter B₁ should have the form
P(b₁-8<B₁ <b₁ + 8) = 0.95
where S = 0.6. The standard deviation of the noise is expected to be σ = 24. Determine the total
number of observations required under each of the following experiment designs:
a. All of the observations are concentrated at the two extreme levels of x in a balanced manner.
b. Observations are distributed uniformly between 20 and 40.
c. An equal number of observations are taken at each of x =
20, 30, and 40.
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