Japan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. The article "Innovative Sludge Handling Through Pelletization Thickening"† reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). Consider the following data.

(a) Compute a 90% CI for 0 + 1251, true average moisture content when the filtration rate is 125. (Round your answers to three decimal places.)

(b) Predict the value of moisture content for a single experimental run in which the filtration rate is 125 using a 90% prediction level. (Round your answers to three decimal places.)

(c) Interpret the hypotheses H0: 0 + 1251 = 80 and Ha: 0 + 1251 < 80.
Carry out a hypothesis test at significance level 0.01.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)