Mating Choice and Offspring Fitness: MiniExperiments Exercise 4.153 explores
the question of whether mate choice improves offspring fitness in fruit flies,
and describes two seemingly identical experiments yielding conflicting results
(one significant, one insignificant). In fact, the second source was actually
a series of three different experiments, and each full experiment was
comprised of 50 different mini-experiments (runs), 10 each on five different
days.
(a) Suppose each of the 50 mini-experiments from the first study were analyzed
individually. If mating choice has no impact on offspring fitness, about how
many of these \(50 \mathrm{p}\) -values would you expect to yield significant
results at \(\alpha=0.05 ?\)
(b) The 50 p-values, testing the alternative \(H_{a}\) :
\(p_{C}>p_{N C}\) (proportion of flies surviving is higher in the mate choice
group) are given below:
$$
\begin{array}{lllllllllll}
\text { Day 1: } & 0.96 & 0.85 & 0.14 & 0.54 & 0.76 & 0.98 & 0.33 & 0.84 &
0.21 & 0.89 \\
\text { Day 2: } & 0.89 & 0.66 & 0.67 & 0.88 & 1.00 & 0.01 & 1.00 & 0.77 &
0.95 & 0.27 \\
\text { Day 3: } & 0.58 & 0.11 & 0.02 & 0.00 & 0.62 & 0.01 & 0.79 & 0.08 &
0.96 & 0.00 \\
\text { Day 4: } & 0.89 & 0.13 & 0.34 & 0.18 & 0.11 & 0.66 & 0.01 & 0.31 &
0.69 & 0.19 \\
\text { Day 5: } & 0.42 & 0.06 & 0.31 & 0.24 & 0.24 & 0.16 & 0.17 & 0.03 &
0.02 & 0.11
\end{array}
$$
How many are actually significant using \(\alpha=0.05 ?\)
(c) You may notice that two p-values (the fourth and last run on day 3 ) are
0.00 when rounded to two decimal places. The second of these is actually
0.0001 if we report more decimal places. This is very significant! Would it be
appropriate and/or ethical to just report this one run, yielding highly
statistically significant evidence that mate choice improves offspring
fitness? Explain.
(d) You may also notice that two of the p-values on day 2 are 1 (rounded to
two decimal places). If we had been testing the opposite alternative, \(H_{a}:\)
\(p_{C}
