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. x 125.5 58.3 201.3 147.5 145.3 124. 112.0 120.0 161.0 179. y 78.0 76.8 81.3 79.8 78.3 78.2 77.3 77.0 80.0 80.1 x 159.4 145. 7 75.0 76.7 151.4 78.1 144.4 79.7 125.1 198.7 77.9 91.5 132.5 159.4 77.1 79.2 110.9 79.7 79.7 79.1 x = 415,849.23, X. - 222,567.41, v2 = 123,991.29. Also, = 140.885, y = 70.73, S, - 18,877.5655, S - 763.976, and SSE = 3.219. The estimated standard deviation is = 0.676 Relevant summary quantities are ) , - 2017.7 - 1574,5 and the equation of the least squares linu isy = 73.090 + 0.040x. Consider the filtration rate-moisture content data introduced above.
(a) Compute a 90% CI for lo + 1208,true average moisture content when the filtration rate is 120. (Round your answers to three decimal places)
(b) Pradict the value of moisture content for a single experimental run in which the filtration rata la 126 using a 90% prediction level. (Round your answers to three decimal places.) How does this interval compare to the interval of part (a)? Why is this the case? The width of the confidence interval in part (a) is - Select the width of the prediction interval in part (b) since the ---Select- interval must account for both the uncertainty in knowing the value of the population mean in addition to the data scatter.
(c) How would the intervals of parts (a) and (b) compare to a CI and PI When filtration rate is 1157 Answer without actually calculating these new intervals. Because the value of 115, denoted by X, is --Select- than 126, the term (7"-72 will be ---Select- , making the standard error --Select , and thus the width of the interval is --Select-
(d) Interpret the hypotheses H: . - 1208, = 90 and : .+ 1208, C90. Assuming the filtration rate is 120 kg-D5/m/h, we would test to see if the average moisture content of the compressed pellets is Select 809 Carry out a hypothesis tast at significanca laval 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.) D-valus -