Problem
In the women's four-person bobsled, the initial times for Run 1 during the recent Sochi games are given in Table below.
Sled Time (secs)
USA 1 55.10
Canada 1 55.22
USA 2 57.90
Belgium 1 60.35
Germany 1 60.80
Netherlands 1 60.85
Russia 1 62.00
Germany 2 62.70
Germany 3 63.00
Switzerland 1 63.25
Average 60.12
Analyses of recent international women's bobsledding competitions have revealed that the correlation between the times of a team's first and second runs is 0.7. Assuming this correlation is equal to the optimal shrinkage estimator coefficient, what is your estimate of the time for the USA 1 sled on Run 2?