Exercises. 1. Specify the rejection region for Spearman’s nonparametric test for rank correlation in each of the following cases

1. Specify the rejection region for Spearman’s nonparametric test for rank correlation in each of the following cases

a)

b)

c)

2. Compute Spearman’s rank correlation coefficient for each of the following pairs of sample observations

a) b)

x	5 20 15 10 3
y	80 83 91 82 87

x	33 61 20 19 40
y	26 36 65 25 35

3. A random sample of nine pairs of observations are recorded on two variables, x and y.

x	19 27 15 35 13 29 16 22 17
y	12 19 7 25 11 10 16 13 18

Do the data provide sufficient evidence to indicate that , the rank correlation between x and y,differs from zero? Test using .

4. Two expert wine testers were asked to rank six brands of wine. Their rankings are shown in the table.

Brand	Expert 1	Expert 2
A B C D E F

Do the data present sufficient evidence to indicate a positive correlation in the rankings of the two experts?

5. Refer to the data of Exercise 6 of the previous section. Find Spearman’s rank correlation coefficient, and use it to test, against two sided alternative, the null hypothesis of no association in the population between this pair of random variables.

6. Refer to the data of Exercise 5 of the previous section. Find Spearman’s rank correlation coefficient, and use it to test the null hypothesis that these quantities are uncorrelated in the population against the alternative that population correlation is negative.

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