Donating Blood to Grandma? Can young blood help old brains? Several studies
\(^{32}\) in mice indicate that it might. In the studies, old mice (equivalent
to about a 70 -year-old person) were randomly assigned to receive blood plasma
either from a young mouse (equivalent to about a 25 -year-old person) or
another old mouse. The mice receiving the young blood showed multiple signs of
a reversal of brain aging. One of the studies \(^{33}\) measured exercise
endurance using maximum treadmill runtime in a 90 -minute window. The number
of minutes of runtime are given in Table 2.17 for the 17 mice receiving plasma
from young mice and the 13 mice receiving plasma from old mice. The data are
also available in YoungBlood.
$$
\begin{aligned}
&\text { Table 2.17 Number of minutes on a treadmill }\\\
&\begin{array}{|l|lllllll|}
\hline \text { Young } & 27 & 28 & 31 & 35 & 39 & 40 & 45 \\
& 46 & 55 & 56 & 59 & 68 & 76 & 90 \\
& 90 & 90 & 90 & & & & \\
\hline \text { Old } & 19 & 21 & 22 & 25 & 28 & 29 & 29 \\
& 31 & 36 & 42 & 50 & 51 & 68 & \\
\hline
\end{array}
\end{aligned}
$$
(a) Calculate \(\bar{x}_{Y},\) the mean number of minutes on the treadmill for
those mice receiving young blood.
(b) Calculate \(\bar{x}_{O},\) the mean number of minutes on the treadmill for
those mice receiving old blood.
(c) To measure the effect size of the young blood, we are interested in the
difference in means \(\bar{x}_{Y}-\bar{x}_{O} .\) What is this difference?
Interpret the result in terms of minutes on a treadmill.
(d) Does this data come from an experiment or an observational study?
(e) If the difference is found to be significant, can we conclude that young
blood increases exercise endurance in old mice? (Researchers are just
beginning to start similar studies on humans.)
