Question

In the 2002 Winter Olympic Games, a scandal rocked the Figure Skating community. A tight competition between Russian pair skaters Elena Berezhnaya and Anton Sikharulidze and Canada’s Jamie Salé and David Pelletier ended in a major judging controversy that resulted in the Russian skaters being awarded the Gold medal and Canadian skaters the Silver medal. It was later determined that the French judge had been pressured to vote for the Russian pair as part of a deal to obtain votes for the French ice dance couple in a later event. Responding to media and public pressure, Salé and Pelletier’s medal was upgraded to a Gold medal, which they shared with the Russian pair skaters. The data describes judges’ scores for the leading pair skaters who competed in the Figure Skating event, for both the short- and long-programs (there were nine judges). Using these data for the 2010 Winter Olympic Games. A complete answer includes setting the null and alternative hypotheses, conducting the test in Excel, drawing conclusion with regard to each hypotheses, and interpreting each result. Use 5% LoS

	J1	J2	J3	J4	J5	J6	J7	J8	J9
Short	7.25	8.5	8.75	8.25	8	7.75	8.25	8.25	8.5
Short	6.75	8.5	8.75	8	8.25	7	8	8	8.25
Short	7	8.75	8.75	8.75	8.5	8.25	8.25	8.25	8.5
Short	7.25	8.5	9	8.25	8.25	8	8.5	8	8.75
Short	6.75	8.5	9	8.5	8.75	8.25	8.5	8.25	8.5
Long	9	9.5	9	8.75	8.25	9	9	8.75	8.75
Long	9.25	9.5	9.25	8.5	8.5	9	9.25	8.75	9
Long	9	9.75	9	8.5	8.5	9	9.25	8.75	9
Long	8.5	9	8.75	9	8.25	9	9	9	8.5
Long	8	9.25	8.75	8.5	8	9	9	8.5	8.5

Answer 1

To analyze the above data we will be using the ANOVA.

Why we are using ANOVA.

Since we want to know about the scandal happened in the scores by judges.Hence,our interest will be to check that each judges' score for every short and long.

And there are 9 judges and two categories Short and long which means we have to consider two way variation in the scores.

Hence,concluding here and we will be using Two-Way Anova without replication.

To test:- (Null Hypothesis)

Hoo: Scores of all judges is same for both canadian and russian

Ho1: Score for both short and long program is same for both canadian and russian

Excel output:-

Data:-

Anova:-

Conclusion:-

Here for both way variation F>Fcritical which implies we reject null hypothesis at 5% los.

i.e All Judges scores is not same for all the categories.

At least one pair is having significant difference in their score and hence scandal can not be proved.