About 2527 athletes competed in the 2002 Olympic Winter Games held at Salt Lake City, Utah, with medals in 78 events. Athletes from 78 nations and territories participated. The following table shows the distribution of gold, silver, and bronze medals awarded to athletes representing the 18 nations who won the most:

Calculate the correlation coefficient and use it and Table 10 in Appendix B to determine a 95% confidence interval on for each of the following cases:

a. Gold and silver

b. Gold and bronze

c. Silver and bronze

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Nation Gold Silver Bronze Germany 12 16 7 USA 10 13 11 Norway 11 7 6 Canada 6 3 8 Austria 2 4 10 Russian Fed. 6 6 4 Italy 4 4 4 France 4 5 2 Switzerland 3 2 6 China 2 2 4 Netherlands 3 5 0 Finland 4 2 1 Sweden 0 2 4 Croatia 3 1 0 Korea 2 2 0 Bulgaria 0 1 2 Estonia 1 1 1 Great Britain 1 0 2