Question 12. Please help Solve this problem. Thanks

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"t 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 125.3 98.0 201.2 147.1 145.8 124.6 112.4 120.1 161.4 179.1 y 77.7 77.0 81.7 79.8 78.3 78.5 77.7 77.0 80.2 80.0 159.5 145.6 75.3 151.2 144.2 124.9 198.7 132.5 159.8 110.9 y 79.9 79.0 76.7 78.0 79.5 78.0 81.3 77.1 79.0 78.6 Relevant summary quantities are * = 2817.6 % - 157 = 1575.0*= 415,828.86, xy, - 222,641.79, Y? - 124,069.90. Also, I = 140,880, 7 = 78.75, 5xx = 18,885.3720, 5x = 755.790, and SSE = 8.418. The estimated standard deviation is a = 0.684 and the equation of the least squares line is y 73.115 + 0.040x. Consider the filtration rate-moisture content data introduced above. (a) Compute a 90% CI for 8, + 125,, 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.) 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 smaller than the width of the prediction interval in part (b) since the prediction V 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 Pt when filtration rate is 115? Answer without actually calculating these new intervals. Because the value of 115, denoted by X*, is farther away from * than 125, the term (** - )2 will be larger making the standard error larger , and thus the width of the interval is wider (c) How would the intervals of parts (a) and (b) compare to a CI and PI when filtration rate is 115? Answer without actually calculating these new intervals. Because the value of 115, denoted by **, is farther away from than 125, the term (** - x)2 will be larger making the standard error larger and thus the width of the interval is wider (d) Interpret the hypotheses Ho: Mo + 1258, - 80 and Ho: lo + 1250,