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\f3. The manager of the purchasing department of a large company would like to develop a regression model to predict the average amount of time it takes to process a given number of invoices. Over a 30day period, data are collected on the number of invoices processed and the total time taken (in hours). The data are available on the book web site in the file invoices.txt. The following model was fit to the data: Y = .60 + lx+e where Y is the processing time and x is the number of invoices. A plot of the data and the fitted model can be found in Figure 2.7. Utilizing the output from the t of this model provided below, com plete the following tasks. (a) Find a 95% condence interval for the startup time, i.e., n. (b) Suppose that a best practice benchmark for the average processing time for an additional invoice is 0.01 hours (or 0.6 minutes). Test the null hypothesis Ha : = 0.01 against a twosided alternative. Interth your result. (c) Find a point estimate and a 95% prediction interval for the time taken to proc ess 130 invoices