n 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 United Kingdom. The analysis used a variety of nitrogen fertilizer applications (kg N/ha), temperature (ºC), 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 σ = 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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

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 United Kingdom. The analysis used a variety of nitrogen
fertilizer applications (kg N/ha), temperature (ºC), 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 σ = 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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution