5.4 Answer parts

(a) through

(e) using (1) the sign-test procedure and (2)

the Wilcoxon signed-rank test procedure.

(a) Test at a significance level not exceeding 0.10 the null hypothesis H0:

M¼2 against the alternative H1:M>2, where Mis the median of the continuous symmetric population from which the random sample

3, 6, 1, 9, 4, 10, 12 is drawn.

(b) Give the exact probability of a type I error in (a).

(c) On the basis of the following random sample of pairs:

X 126 131 153 125 119 102 116 163 Y 120 126 152 129 102 105 100 175 test at a significance level not exceeding 0.10 the null hypothesis H0 :M¼2 against the alternative H1 M 6¼ 2, where M is the median of the continuous and symmetric population of differences D¼XY.

(d) Give the exact probability of a type I error in (c).

(e) Give the confidence interval corresponding to the test in (c).