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

46

seconds with a standard deviation of

19

seconds, while a random sample of

9

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. (If necessary, consult a list of formulas.)

(a)	State the null hypothesis H0 and the alternative hypothesis H1 .
H0: this needs to say u1-u2=0
H1:??
(b)	Determine the type of test statistic to use.
	(Choose one)
(c)	Find the value of the test statistic. (Round to three or more decimal places.)
(d)	Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.)
(e)	Can we conclude that the mean processing time of computer 1 is less than the mean processing time of computer 2?
Yes No