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?
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
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
(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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