Question: As a basis for a brochure describing the speed of a new computer system, you have measured how long it takes the machine to complete a particular benchmark database program. Since the state of the disks in the database is constantly changing as records are added, changed, and deleted, there is some variation in the test results. Here are times, in minutes, for 14 independent repetitions of this testing procedure:

5, 6, 8, 11, 5, 8, 11, 10, 6, 10, 5, 9, 5, 5

a. Find the two-sided 95% confidence interval and describe its meaning in terms of the long-run mean performance of the system.

b. Find the appropriate one-sided 95% confidence interval, assuming you wish to show off how fast the system is (so that lower numbers are better).

c. Find the appropriate one-sided 90% confidence interval.

d. Find the appropriate one-sided 99% confidence interval.

e. Write a brief paragraph for an advertising brochure describing one (or more) of the preceding results. Be honest, but put your "best foot forward, " and write in simple English. Include a technical footnote, if necessary, so that technically knowledgeable people can tell what you really did.