91影视

Given:

When testing null hypothesis

\({H_0}:{\mu _1} - {\mu _2} = {\Delta _0}\)

versus one of the alternative hypothesis, one could use test statistic value

\(w = \sum\limits_{i = 1}^m {{r_i}} \)

where\({r_i}\)is rank of\(\left( {{x_i} - {\Delta _0}} \right)\) in the combined sample of\(m + n{\left( {x - {\Delta _0}} \right)^\prime }\)s and\({y^\prime }\)s.

The\(P\)-value depends on alternative hypothesis
Alternative\({{\rm{H}}_y}\)pothesis\({P_{{\rm{ - value }}}}\)

\(\begin{array}{*{20}{l}}{{H_a}:{\mu _1} - {\mu _2} > {\Delta _0}}&{{P_0}(W \ge w)}\\{{I_a}:{\mu _1} - {\mu _2} < {\Delta _0}}&{{P_0}(W \le w) = {P_0}(W \ge m(mn + n + 1) - w)}\\{{I_a}:{\mu _1} - {\mu _2} \ne {\Delta _0}}&{2{P_0}(W \ge \max \{ w,m(m + n + 1) - w)}\end{array}\)

Use Table\(A.14\)to determine\(P\)-values (use closest value to corresponding significance level to make conclusions).
The null hypotheses of interest are

\({H_0}:{\mu _1} - {\mu _2} = - 25\)

versus alternative hypothesis

\({H_a}:{\mu _1} - {\mu _2} < - 25,\)

The following table represents required data to compute test statistic value.

The alternative hypothesis is lower-sided; thus, the\(P\)-value is

\({P_0}(W \le w) = {P_0}(W \ge m(m + n + 1) - w) = {P_0}(W \ge 73)\)

Using the table in appendix, for

\(\begin{array}{l}\alpha = 0.05,\\m = 7,\\n = 8,\end{array}\)

\(P\)value is

\({P_0}(W \ge 73) = 0.027,\)

the corresponding\(P\)-value is less than\(0.05\).

Hence,reject null hypothesisat given significance level, the true average level for exposed infants appears to exceed the unexposed infants by more than
25.

Do not reject null hypothesis at significance level \({\rm{0}}{\rm{.01}}\) .