Question

3.6 Establish nominal 95 percent confidence intervals for the median based on the Wilcoxon signed-rank test for the following data sets. If an appropriate computer program is available use it to comment on the discontinuities at the end points of your estimated intervals based on Walsh averages.

Set I    1   1 1 1 1 3 3   5   5 7 7

Set II 1   2 2 4 4 4 4 5 5   5 7

Answer 1

here I write R-code for given problem as

x=c(1,1,1,1,1,3,3,5,5,7,7)

y=c(1,2,2,4,4,4,4,5,5,5,7)

wilcox.test(x, y, conf.int=T)

And the Output is as follows

Wilcoxon rank sum test with continuity correction

data:  x and y
W = 46.5, p-value = 0.3656
alternative hypothesis: true location shift is not equal to 0
95 percent confidence interval:
 -3.000068  1.000009
sample estimates:
difference in location 
            -0.9999629

Thus from above output we get confidence interval as

[-3.000068, 1.000009]