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 8 processing times from computer 1 showed a mean of 45 seconds with a standard deviation of 19 seconds, while a random sample of 10 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 54 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 u,, the mean processing time of computer 1, is less than u,, 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 H, and the alternative hypothesis H,. H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (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? OYes ONo
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 8 processing times from computer 1 showed a mean of 45 seconds with a standard deviation of 19 seconds, while a random sample of 10 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 54 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 u,, the mean processing time of computer 1, is less than u,, 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 H, and the alternative hypothesis H,. H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (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? OYes ONo
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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 8 processing times from computer 1 showed a mean of 45 seconds with a standard deviation of 19 seconds, while a random
sample of 10 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 54 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 u, the mean processing time of computer 1, is less than , 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 H, and the alternative hypothesis H .
H :0
:0
(b) Determine the type of test statistic to use.
(Choose one) ▼
OSO
(c) Find the value of the test statistic. (Round to three or more decimal places.)
O<O
(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?
O Yes ONo
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