Reports Are Available on a Study in Which Various Measurements$$\begin{array} { l c c c c c c c c }
\hline \text { Unexposed } & 8 & 11 & 12 & 14 & 20 & 43 & 111 & \
\hline \text { Exposed } & 35 & 56 & 83 & 92 & 128 & 150 & 176 & 208 \
\hline
\end{array}$$

Question

Reports Are Available on a Study in Which Various Measurements$$\begin{array} { l c c c c c c c c } 
\hline \text { Unexposed } & 8 & 11 & 12 & 14 & 20 & 43 & 111 & \
\hline \text { Exposed } & 35 & 56 & 83 & 92 & 128 & 150 & 176 & 208 \
\hline
\end{array}$$

Examlex · Accepted Answer

The Answer is Let

\mu _ { 1 } ext { and } \mu _ { 2 }

denote true average cotanine levels in unexposed and exposed infants, respectively. The hypotheses of interest are

H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = - 25 ext { vs. } H _ { \pm } : \mu _ { 1 } - \mu _ { 2 } , - 25

With m = 7, n = 8,

H _ { o }

will be rejected at level .05 if

w \leq 7 ( + 8 + 1 ) - 71 = 41

Before ranking, -25 is subtracted from each

x _ { 1 }

(i.e. 25 is added to each), giving 33, 36, 37, 39, 45, 68, and 136. The corresponding ranks in the combined set of 15 observations are 1, 3, 4, 5, 6, 8, and 12, from which w = 1 + 3 + … + 12 = 39. Because

39 \leq 41 , H _ { o }

is rejected. The true average level for exposed infants appears to exceed that for unexposed infants by more than 25 (note that

H _ { o }

would not be rejected using level .01).

Reports Are Available on a Study in Which Various Measurements

Definitions: