Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. An article in the Journal of Agricultural Science ["The Use of Residual Maximum Likelihood to Model Grain Quality Characteristics of Wheat with Variety, Climatic and Nitrogen Fertilizer Effects" (1997, Vol. 128, pp. 135-142)] investigated means of wheat grain crude protein content (CP) and Hagberg falling number (HFN) surveyed in the UK. The analysis used a variety of nitrogen fertilizer applications (kg N/ha), temperature (°C), and total monthly rainfall (mm). The data shown below describe temperatures for wheat grown at Harper Adams Agricultural College between 1982 and 1993. The temperatures measured in June were obtained as follows: 14.1 15.8 15.5 13.9 13.7 13.3 13.6 15.7 14.3 13.1 14.5 Assume that the population has a normal distribution and the standard deviation is known to be o = 0.7. (a) Construct a 99% two-sided confidence interval on the mean temperature. Round to two decimal places (e.g. 98.76). i
Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. An article in the Journal of Agricultural Science ["The Use of Residual Maximum Likelihood to Model Grain Quality Characteristics of Wheat with Variety, Climatic and Nitrogen Fertilizer Effects" (1997, Vol. 128, pp. 135-142)] investigated means of wheat grain crude protein content (CP) and Hagberg falling number (HFN) surveyed in the UK. The analysis used a variety of nitrogen fertilizer applications (kg N/ha), temperature (°C), and total monthly rainfall (mm). The data shown below describe temperatures for wheat grown at Harper Adams Agricultural College between 1982 and 1993. The temperatures measured in June were obtained as follows: 14.1 15.8 15.5 13.9 13.7 13.3 13.6 15.7 14.3 13.1 14.5 Assume that the population has a normal distribution and the standard deviation is known to be o = 0.7. (a) Construct a 99% two-sided confidence interval on the mean temperature. Round to two decimal places (e.g. 98.76). i
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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![Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise.
An article in the Journal of Agricultural Science ["The Use of Residual Maximum Likelihood to Model Grain Quality Characteristics of
Wheat with Variety, Climatic and Nitrogen Fertilizer Effects" (1997, Vol. 128, pp. 135-142)] investigated means of wheat grain crude
protein content (CP) and Hagberg falling number (HFN) surveyed in the UK. The analysis used a variety of nitrogen fertilizer
applications (kg N/ha), temperature (°C), and total monthly rainfall (mm). The data shown below describe temperatures for wheat
grown at Harper Adams Agricultural College between 1982 and 1993. The temperatures measured in June were obtained as follows:
14.1
15.8
15.5
13.9
13.7
13.3
13.6
15.7
14.3
13.1
14.5
Assume that the population has a normal distribution and the standard deviation is known to be o = 0.7.
(a) Construct a 99% two-sided confidence interval on the mean temperature. Round to two decimal places (e.g. 98.76).
i
<us i
(b) Construct a 95% lower-confidence bound on the mean temperature. Round to two decimal places (e.g. 98.76).
i
(c) Suppose that we wanted to be 95% confident that the error in estimating the mean temperature is less than 2 degrees Celsius.
What sample size should be used?
n =
(d) Suppose that we wanted the total width of the two-sided confidence interval on mean temperature to be 1.5 degrees Celsius at
95% confidence. What sample size should be used?
n =
i](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79aebaec-25e6-48b5-901e-6cb6827148d8%2Fb1fdaca2-c30a-4131-825b-11057b72752a%2Fgkfii6g_processed.png&w=3840&q=75)
Transcribed Image Text:Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise.
An article in the Journal of Agricultural Science ["The Use of Residual Maximum Likelihood to Model Grain Quality Characteristics of
Wheat with Variety, Climatic and Nitrogen Fertilizer Effects" (1997, Vol. 128, pp. 135-142)] investigated means of wheat grain crude
protein content (CP) and Hagberg falling number (HFN) surveyed in the UK. The analysis used a variety of nitrogen fertilizer
applications (kg N/ha), temperature (°C), and total monthly rainfall (mm). The data shown below describe temperatures for wheat
grown at Harper Adams Agricultural College between 1982 and 1993. The temperatures measured in June were obtained as follows:
14.1
15.8
15.5
13.9
13.7
13.3
13.6
15.7
14.3
13.1
14.5
Assume that the population has a normal distribution and the standard deviation is known to be o = 0.7.
(a) Construct a 99% two-sided confidence interval on the mean temperature. Round to two decimal places (e.g. 98.76).
i
<us i
(b) Construct a 95% lower-confidence bound on the mean temperature. Round to two decimal places (e.g. 98.76).
i
(c) Suppose that we wanted to be 95% confident that the error in estimating the mean temperature is less than 2 degrees Celsius.
What sample size should be used?
n =
(d) Suppose that we wanted the total width of the two-sided confidence interval on mean temperature to be 1.5 degrees Celsius at
95% confidence. What sample size should be used?
n =
i
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