1. Mutual funds often compare their performance with a benchmark provided by an "index" that describes the performance of the class of assets in which the fund invests. For example, the Vanguard International Growth Fund benchmarks its performance against the EAFE (Europe, Australasia, Far East) index. The table below gives the annual returns (percent) for the fund and the index. Does the fund's performance differ significantly from that of its benchmark?
(a) Explain clearly why the matched pairs t test is the proper choice to answer this question.
(b) Do a complete analysis for the question that is posed here.
4. The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25 right-handed students to turn a knob (with their right hands) that moved an indicator by screw action. There were two identical instruments, one with right-hand thread (the knob turns clockwise) and the other with a left-hand thread (the knob turns counterclockwise). The table below gives the times in seconds each subject took to move the indicator a fixed distance.
(a) Each of the 25 students used both instruments. Discuss briefly how you would use randomization in arranging the experiment.
(b) The project hoped to show that right-handed people find right-hand threads easier to use. Do an analysis that leads to a conclusion about this issue.
