Question

 A random sample of 12 financial analysts was asked to predict the percentage increases in the prices of two common stocks over the next year. The data are: 

Analyst: A, B, C, D, E, F, G, H, I, J

Stock 1: 6.8, 9.8, 2.1, 6.2, 7.1, 6.5, 9.3, 1.0, -0.2,9.6

Stock 2: 6.2, 12.3, 5.3, 6.8, 7.0, 6.2, 10.1, 2.7, 1.3, 9.8 

Use the sign test and Wilcoxon sign rank test to test the null hypothesis that, for the population of analysts there is no overall preference for increases in one stock over the other.

Answer 1

The null and alternative hypotheses are as follows

$H_0: \mu_1=\mu_2$

(There is no overall preference for increases in one stock over the other)

$H_1: \mu_1≠ \mu_2$

(There is an overall preference for increases in one stock over the other)

From above table n = 10

$T_+=5+1+3=9 \\ T_- = 9+10+4+6+8+7+2= 46$

In Wilcoxon Signed-Rank $w_{stat}$ is the smaller of $T_+$ and $T_-$ .

$w_{stat}= 9 \\ α=0.05$

Two-tailed test

From Wilcoxon Signed-Ranks Table

$w_{crit} = 8 \\ w_{stat}>w_{crit}$

Accept $H_0$ .

There is an overall preference for increases in one stock over the other.