Use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of α=0.01 Two judges ranked seven bands in a finals competition of marching bands (Coppell, Keller, Grapevine, Dickinson, Poteet, Fossil Ridge, Heritage), and their rankings are listed below. Test for a correlation between the two judges. Do the judges appear to rank about the same or are they very different?
Band 
Cpl 
Klr 
Grp 
Dck 
Ptt 
FR 
Her 


First Judge 
6 
5 
3 
2 
4 
7 
1 

Third Judge 
4 
5 
7 
2 
3 
6 
1 
What are the null and alternative hypotheses
Calculate the test statistic. rs equals=
Find the critical values. rs = ±
Do the judges appear to rank about the same or are they very different?
(Reject or Fail to Reject) Ho. There (is or is not) sufficient evidence to support the claim of a correlation between the two judges. The two judges appear to (rank the bands very differently, have opposite rankings, rank the bands about the same)
Band  First judge  Second Judge  d^2 

Cpl  6  4  4 
Klr  5  5  0 
Grp  3  7  16 
Dck  2  2  0 
Ptt  4  3  1 
FR  7  6  1 
Her  1  1  0 
Total  22 
Spearman Rank Correlation is given by,
The null and alternnative hypothesis are,
The test statistic equals,
The critical value is given by,
Failed to reject H_{0}. There is sufficient evidence to support the claim of a correlation between the two judges appear to rank the bands very differently.
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