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 14 processing times from computer 1 showed a mean of 36 seconds with a standard deviation of 16

seconds, while a random sample of 12 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 50 seconds with a standard deviation of 15 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 1 , the mean processing time of computer 1, is less than 2 , the mean processing time of computer 2?

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

Questions

Find the value of the test statistic. (Round to three or more decimal places.)

Find the p-value round to three or more decimal places