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), tempera- ture (C), and total monthly rainfall (mm). The data shown be- low describe temperatures for wheat grown at Harper Adams Agricultural College between 1982 and 1993. The tempera- tures measured in June were obtained as follows: 15.2 14.3 14.2 14.2 14.0 13.5 12.2 11.8 144 125 15.2 Assume that the standard deviation is known to be or 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 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?

(d) Suppose that we wanted the total width of the two-sided con- fidence interval on mean temperature to be 1.5 degrees Celsius at 95% confidence. What sample size should be used?