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The university data center has two main computers: computer 1 and computer 2. A new routine has recently been written for computer 1 to handle its tasks, while computer 2 is still using the preexisting routine. The center wants to determine if the processing time for computer 1's tasks is now less than that of computer 2. A random sample of 10 processing times from computer 1 showed a mean of 38 seconds with a standard deviation of 20 seconds, while a random sample of 8 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 61 seconds with a standard deviation of 19 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that , the mean processing time of computer 1, is less than j,, the mean processing time of computer 27 Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of (formulas.) (a) State the null hypothesis Ho and the alternative hypothesis . H S (b) Determine the type of test statistic to use. (Choose one) 0-0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0#0 00 X ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean processing time of computer 1 is less than the mean processing time of computer 27 OYes ONo