4. [Ocean Weather] Information about ocean weather can be extracted from radar returns with the aid of a special algorithm. A study is conducted to estimate the difference in wind speed as measured on the ground and via the Seasat satellite. To do so, wind speeds (miles per hour) are measured on the ground and via the Seasat satellite simultaneously at 12 special times. The data is shown in the following table. The table also shows the difference between the wind speed on the ground and that via the Seasat satellite at each time, as well as some summary statistics.
4. [Ocean Weather] Information about ocean weather can be extracted from radar returns with the aid of a special algorithm. A study is conducted to estimate the difference in wind speed as measured on the ground and via the Seasat satellite. To do so, wind speeds (miles per hour) are measured on the ground and via the Seasat satellite simultaneously at 12 special times. The data is shown in the following table. The table also shows the difference between the wind speed on the ground and that via the Seasat satellite at each time, as well as some summary statistics.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text:Please use the t-table provided at the end of this exam to find a range of the p-value for your test
statistic.
What is your conclusion based on the test? Use a = 0.05 as the significance level. Explain your
answer.
![4. [Ocean Weather]
Information about ocean weather can be extracted from radar returns with the aid of a special algorithm. A
study is conducted to estimate the difference in wind speed as measured on the ground and via the Seasat
satellite. To do so, wind speeds (miles per hour) are measured on the ground and via the Seasat satellite
simultaneously at 12 special times. The data is shown in the following table. The table also shows the difference
between the wind speed on the ground and that via the Seasat satellite at each time, as well as some summary
statistics.
Difference
Time
Ground (x) Satellite (y) d= x – y
1
4.46
4.08
0.38
3.99
3.94
0.05
3
3.73
5.00
-1.27
4
3.29
5.20
-1.91
4.82
3.92
0.90
6
6.71
6.21
0.50
7
4.61
5.95
-1.34
8.
3.87
3.07
0.80
3.17
4.76
-1.59
10
4.42
3.25
1.17
11
3.76
4.89
-1.13
12
3.30
4.80
-1.50
d = -0.41
Sd = 1.14
It is claimed that the wind speed measured on the ground is lower than that measured via the
Satellite on average. Set up your hypotheses to test this claim. Be sure to define the parameters you used
in the test.
Write down the formula of the t statistic for the test in Part (a) and calculate the value of the test
statistic based on the observed data. Keep the second decimal place in your final answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42f9d7c6-4c7a-44ab-8c36-1d379ff2d1eb%2Fe867dc3e-fac8-435c-bc60-3af122159a1e%2Fde808ee_processed.png&w=3840&q=75)
Transcribed Image Text:4. [Ocean Weather]
Information about ocean weather can be extracted from radar returns with the aid of a special algorithm. A
study is conducted to estimate the difference in wind speed as measured on the ground and via the Seasat
satellite. To do so, wind speeds (miles per hour) are measured on the ground and via the Seasat satellite
simultaneously at 12 special times. The data is shown in the following table. The table also shows the difference
between the wind speed on the ground and that via the Seasat satellite at each time, as well as some summary
statistics.
Difference
Time
Ground (x) Satellite (y) d= x – y
1
4.46
4.08
0.38
3.99
3.94
0.05
3
3.73
5.00
-1.27
4
3.29
5.20
-1.91
4.82
3.92
0.90
6
6.71
6.21
0.50
7
4.61
5.95
-1.34
8.
3.87
3.07
0.80
3.17
4.76
-1.59
10
4.42
3.25
1.17
11
3.76
4.89
-1.13
12
3.30
4.80
-1.50
d = -0.41
Sd = 1.14
It is claimed that the wind speed measured on the ground is lower than that measured via the
Satellite on average. Set up your hypotheses to test this claim. Be sure to define the parameters you used
in the test.
Write down the formula of the t statistic for the test in Part (a) and calculate the value of the test
statistic based on the observed data. Keep the second decimal place in your final answer.
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