8. Suppose the scientists have collected the following data: n = 6 m = 11 0.0003 0.0001 Is there sufficient evidence to conclude that the Webb space telescope has smaller measurement error compared to the Bubble space telescope with significance level α = 0.1? Use [Hint_2] for computing the relevent quantiles of the F distribution in Julia. 9. Use the interactive widget in [Hint_3] below to find the (approximate) p-value associated with the value of Ô from part#8.
8. Suppose the scientists have collected the following data: n = 6 m = 11 0.0003 0.0001 Is there sufficient evidence to conclude that the Webb space telescope has smaller measurement error compared to the Bubble space telescope with significance level α = 0.1? Use [Hint_2] for computing the relevent quantiles of the F distribution in Julia. 9. Use the interactive widget in [Hint_3] below to find the (approximate) p-value associated with the value of Ô from part#8.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I want to know the answer and details step by step
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![8.
Suppose the scientists have collected the following data:
n = 6
m
=
=
11
0.0003
0.0001
Is there sufficient evidence to conclude that the Webb space telescope has smaller measurement error
compared to the Bubble space telescope with significance level α = 0.1?
Use [Hint_2] for computing the relevent quantiles of the F distribution in Julia.
9.
Use the interactive widget in [Hint_3] below to find the (approximate) p-value associated with the
value of Ô from part#8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7c2748e-5ba1-4f2f-bc7d-c6e1ab8bba12%2F30009fd2-ae38-47d6-8bc9-a8921dbfa867%2Fg7zrudl_processed.png&w=3840&q=75)
Transcribed Image Text:8.
Suppose the scientists have collected the following data:
n = 6
m
=
=
11
0.0003
0.0001
Is there sufficient evidence to conclude that the Webb space telescope has smaller measurement error
compared to the Bubble space telescope with significance level α = 0.1?
Use [Hint_2] for computing the relevent quantiles of the F distribution in Julia.
9.
Use the interactive widget in [Hint_3] below to find the (approximate) p-value associated with the
value of Ô from part#8.
![In this question, we will set up and test the appropriate hypothesis for verifying a claim from
astronomy.
• The Bubble space telescope is an optical telescope that was launched into space in
1990 to collect data from distant stars and glaxies, and has proven to be an
invaluable source of information to many astronomers and cosmologists.
• Recently, a team of researchers from NASA led the design and development of the
Webb space telescope, which was claimed to be capable of higher resolution images
and less error-prone in comparison to its predecesor, the Bubble space telescope.
• In order to lend credence to the claim that the newly designed Webb space telescope was
capable of more accurate measurements compared to the Bubble space telescope, the
scientists from NASA were required to show sufficient evidence for this claim in a
formal statistical setting.
In order to test the hypothesis that the measurement error from the Webb telescope was indeed smaller
than the measurement error from the Bubble telescope, the researchers designed the following
experiment:
A collection of n and m observations were taken of a fixed object in the observable universe by, the
Bubble telescope and the Webb telescope, respectively.
Let
X1, X2,..., XN(μ,0²)
denote the collection of n observations taken by the Bubble Telescope, and let
Y₁, Y2,..., YmN(μ, o)
denote the collection of n observations taken by the Webb Telescope. The mean is the true
(unknown) brightness of the object, and the (unknown) variances o and o represent the
measurement error from the Bubble and Webb telescopes, respectively.
Using this information, answer the following questions:
[Hint_2]
In Julia, the F-distribution can be specified using FDist(). For example, if we want to specify
Y~ F2,3, the F-Distribution with 2 numerator degrees of freedom and 3 denominator degrees
of freedom, then
n = 2
m = 3
Y = FDist(n, m)
Having specified the distribution Y = F2,3, we can use the cdf() function to compute the CDF
Fy (y) for some y where
Fy(y) = P(Y ≤y)
and the quantile() function to compute the quantile Y₁-a where
P(Y≥ Y₁-a) = a
# CDF: F_Y(y)
y = 2.9; cdf (Y, y)
# Quantile: Y_{1-a}
x = 0.05; quantile(Y, 1-a)
[Hint 3]
• Input your value of a here 1.0
1.00
0.75
0.50
0.25
0.00
0
n
25
m
F24.24
25
3
a
0.009
(F> F-1-1)
FA-1-1
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7c2748e-5ba1-4f2f-bc7d-c6e1ab8bba12%2F30009fd2-ae38-47d6-8bc9-a8921dbfa867%2Fn3jhuwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this question, we will set up and test the appropriate hypothesis for verifying a claim from
astronomy.
• The Bubble space telescope is an optical telescope that was launched into space in
1990 to collect data from distant stars and glaxies, and has proven to be an
invaluable source of information to many astronomers and cosmologists.
• Recently, a team of researchers from NASA led the design and development of the
Webb space telescope, which was claimed to be capable of higher resolution images
and less error-prone in comparison to its predecesor, the Bubble space telescope.
• In order to lend credence to the claim that the newly designed Webb space telescope was
capable of more accurate measurements compared to the Bubble space telescope, the
scientists from NASA were required to show sufficient evidence for this claim in a
formal statistical setting.
In order to test the hypothesis that the measurement error from the Webb telescope was indeed smaller
than the measurement error from the Bubble telescope, the researchers designed the following
experiment:
A collection of n and m observations were taken of a fixed object in the observable universe by, the
Bubble telescope and the Webb telescope, respectively.
Let
X1, X2,..., XN(μ,0²)
denote the collection of n observations taken by the Bubble Telescope, and let
Y₁, Y2,..., YmN(μ, o)
denote the collection of n observations taken by the Webb Telescope. The mean is the true
(unknown) brightness of the object, and the (unknown) variances o and o represent the
measurement error from the Bubble and Webb telescopes, respectively.
Using this information, answer the following questions:
[Hint_2]
In Julia, the F-distribution can be specified using FDist(). For example, if we want to specify
Y~ F2,3, the F-Distribution with 2 numerator degrees of freedom and 3 denominator degrees
of freedom, then
n = 2
m = 3
Y = FDist(n, m)
Having specified the distribution Y = F2,3, we can use the cdf() function to compute the CDF
Fy (y) for some y where
Fy(y) = P(Y ≤y)
and the quantile() function to compute the quantile Y₁-a where
P(Y≥ Y₁-a) = a
# CDF: F_Y(y)
y = 2.9; cdf (Y, y)
# Quantile: Y_{1-a}
x = 0.05; quantile(Y, 1-a)
[Hint 3]
• Input your value of a here 1.0
1.00
0.75
0.50
0.25
0.00
0
n
25
m
F24.24
25
3
a
0.009
(F> F-1-1)
FA-1-1
4
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