A computer technology firm wishes to check whether the speed of a new processor exceeds that of an existing processor when used in one of its popular laptop computer models. Accordingly, it measures the time required to complete seven common tasks on two otherwise identical computers, one with the new processor and one with the existing processor. The time required is as follows:
Task Time Required with Time Required with
New Processor (seconds) Existing Processor (seconds)
1..................1.47................................1.68
2..................2.59................................2.99
3..................5.21................................5.69
4..................3.49................................3.75
5..................3.99................................4.25
6..................3.10................................2.99
7..................5.75................................6.19
a. Specify the null and alternative hypotheses to test whether the time required for the new processor is less than the existing processor.
b. At the 5% significance level, what is the critical value(s)? What is the decision rule?
c. Assuming that the difference in time is normally distributed, calculate the value of the test statistic.
d. Based on the above results, is the new processor faster than the old processor?