c_.___ .. t DETAILS Devonesrnrs 12.4.045. ASK YOUR TEACHER I PM\":11\"Mama5 Japan's high population denSIty has resulted in a multitude of resourcetusage problems. One especially serious difficulty concerns waste removal. The article "Innovative Sludge Handling Through Pelletlzation 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 ltration rate (x, In kg-DSlthr). Consider the following data. x 125.4 98.4 201.2 147.3 146.0 124.6 112.3 120.4 161.1 179.0 y 77.9 76.6 81.5 79.6 78.0 78.3 77.3 77.2 79.9 80.3 x 159.6 145.6 74.9 151.3 144.3 124.8 1990 132.5 159.8 110.7 79.3 78.8 76.9 78.1 79.4 78.1 81.7 77.0 79.2 Relevantsurnmary quantities are 2x} = 2818.2 Zyi = 1574.1, 2x,2 = 415,047.80, Zx'yi = 222,591.33, Zyjz = 123,929.95. Also, = 140.910, )7 = 78.71, Sxx = 18,935.2380, 5\": 784.899, and SSE = 3.229. The estimated standard deviation is a' = 0.676 and the equation of the least squares line is y = 72.928 + 0.041x. Consider the ltration rate-moisture content data introduced above. (a) Compute a 90% CI for '30 + 126,31, true average moisture content when the ltration rate is 126. (Round your answers to three decimal places.) (DIE) (b) Predict the value of moisture content for a single experimental run in which the filtration rate is 126 using a 90% prediction level. (Round your answers to three decimal places.) 0:] - |:]) How does this interval compare to the interval of part (a)? Why is this the case? The width of the condence interval in part (a) is the width of the prediction interval in part (b) since the l~Select-- 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 pars (a) and (b) compare to a CI and PI when ltration rate is 115? Answer without actually calculating these new intervals. Because the value of 115, denoted by x', is )7 than 126, the term (x' )2 will be , making the standard error , and thus the width ofme interval 1S . Wenchypoeiem Ho: pa + 125,91 = so and Ha: p0 + 126,51