Bond-market investors, like stock-market investors, often choose their investment managers on the basis of the manager's past performance. Kritzman has reported on a statistical analysis performed by the Bell System on its bond managers. The purpose of the analysis was to determine the extent to which a manager's past performance was a good predictor of future performance and if there was a difference in performance in two chosen periods

The study involved 32 Bell System bond managers, for each of whom 10 years of data were available. Each manager was assigned a percentile ranking for both the 1972-1976 period and the 1977-1981 period, based on the performance of the manager's bond portfolio relative to the performance of the competition's portfolios. These percentile rankings are shown in the accompanying table. The data are also stored in column 1 (1972-1976 percentile rankings) and column 2 (1977-1981 percentile rankings).

On the basis of the data presented, what would you conclude about the consistency in performance of the Bell System bond managers? Specifically,

1. Test the equality of variance of the 1972-1976 period and the 1977-1981 period, do not consider the influence of the manager.
2. Test the equality of means of the 1972-1976 period and the 1977-1981 period, do not consider the influence of the manager.
3. Consider a matched or dependent design, where the influence of the manager is important, test the means of the 1972-1976 period and the 1977-1981 period.
4. Test if there is a positive correlation between the two periods.