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+ Go Tutorial An article in the Journal of Agricul- Science [The Use of Residual Maximum Likelihood to 1 Grain Quality Characteristics of Wheat with Variety, atic and Nitrogen Fertilizer Effects" (1997, Vol. 128, pp. |42)] investigated means of wheat grain crude protein nt (CP) and Hagberg falling number (HFN) surveyed in nited Kingdom. The analysis used a variety of nitrogen zer applications (kg N/ha), temperature (°C), and total nly rainfall (mm). The following data below describe eratures for wheat grown at Harper Adams Agricultural

+ Go Tutorial An article in the Journal of Agricul- Science [The Use of Residual Maximum Likelihood to 1 Grain Quality Characteristics of Wheat with Variety, atic and Nitrogen Fertilizer Effects" (1997, Vol. 128, pp. |42)] investigated means of wheat grain crude protein nt (CP) and Hagberg falling number (HFN) surveyed in nited Kingdom. The analysis used a variety of nitrogen zer applications (kg N/ha), temperature (°C), and total nly rainfall (mm). The following data below describe eratures for wheat grown at Harper Adams Agricultural

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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a) 99% two sided CI on the mean temperature Z.2 = Z0.00s = 2.57, and = 13.77, o = 0.5, n=11 |susi+Z0,009 Vn vn 0.5 13.77 - 2.57 <μ= 13.77+ 2.57 | 0.5 J11 13.383μ< 14.157 b) 95% lower-confidence bound on the mean temperature For a = 0.05, z. = zaos =1.65 and I= 13.77, o = 0.5, n =11 0.5 13.77-1.65 13.521 s u c) 95% confidence that the error of estimating the mean temperature for wheat grown is less than 2 degrees Celsius. For a = 0.05, z2 = z0.02s = 1.96, and o = 0.5, E = 2 2 (1.96(0.5)) n = E = 0.2401 Always round up to the next number, therefore n = 1. d) Set the width to 1.5 degrees Celsius with o = 0.5, za.025 = 1.96 solve for n. 1/2 width = (1.96)(0.5)/n = 0.75 0.98 = 0.75 n 0.98 =1.707 0.75 Therefore, n = 2.
Transcribed Image Text:a) 99% two sided CI on the mean temperature Z.2 = Z0.00s = 2.57, and = 13.77, o = 0.5, n=11 |susi+Z0,009 Vn vn 0.5 13.77 - 2.57 <μ= 13.77+ 2.57 | 0.5 J11 13.383μ< 14.157 b) 95% lower-confidence bound on the mean temperature For a = 0.05, z. = zaos =1.65 and I= 13.77, o = 0.5, n =11 0.5 13.77-1.65 13.521 s u c) 95% confidence that the error of estimating the mean temperature for wheat grown is less than 2 degrees Celsius. For a = 0.05, z2 = z0.02s = 1.96, and o = 0.5, E = 2 2 (1.96(0.5)) n = E = 0.2401 Always round up to the next number, therefore n = 1. d) Set the width to 1.5 degrees Celsius with o = 0.5, za.025 = 1.96 solve for n. 1/2 width = (1.96)(0.5)/n = 0.75 0.98 = 0.75 n 0.98 =1.707 0.75 Therefore, n = 2.
8-21. O Go Tutorial An article in the Journal of Agricul- tural 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 United Kingdom. The analysis used a variety of nitrogen fertilizer applications (kg N/ha), temperature (°C), and total monthly rainfall (mm). The following data below describe temperatures for wheat grown at Harper Adams Agricultural College between 1982 and 1993. The temperatures measured in June were obtained as follows: 15.2 14.2 14.0 12.2 14.4 12.5 14.3 14.2 13.5 11.8 15.2 Assume that the standard deviation is known to be o = 0.5. (a) Construct a 99% two-sided confidence interval on the mean temperature. (b) Construct a 95% lower-confidence bound on the mean temperature. (c) Suppose that you 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? (d) Suppose that you 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?
Transcribed Image Text:8-21. O Go Tutorial An article in the Journal of Agricul- tural 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 United Kingdom. The analysis used a variety of nitrogen fertilizer applications (kg N/ha), temperature (°C), and total monthly rainfall (mm). The following data below describe temperatures for wheat grown at Harper Adams Agricultural College between 1982 and 1993. The temperatures measured in June were obtained as follows: 15.2 14.2 14.0 12.2 14.4 12.5 14.3 14.2 13.5 11.8 15.2 Assume that the standard deviation is known to be o = 0.5. (a) Construct a 99% two-sided confidence interval on the mean temperature. (b) Construct a 95% lower-confidence bound on the mean temperature. (c) Suppose that you 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? (d) Suppose that you 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?
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