Question

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)

Answer 1

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 H₀. 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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