Female primates visibly display their fertile window, often with red or pink
coloration. Do humans also do this? A study \(^{18}\) looked at whether human
females are more likely to wear red or pink during their fertile window (days
\(6-14\) of their cycle \()\). They collected data on 24 female undergraduates at
the University of British Columbia, and asked each how many days it had been
since her last period, and observed the color of her shirt. Of the 10 females
in their fertile window, 4 were wearing red or pink shirts. Of the 14 females
not in their fertile window, only 1 was wearing a red or pink shirt.
(a) State the null and alternative hypotheses.
(b) Calculate the relevant sample statistic, \(\hat{p}_{f}-\hat{p}_{n f}\), for
the difference in proportion wearing a pink or red shirt between the fertile
and not fertile groups.
(c) For the 1000 statistics obtained from the simulated randomization samples,
only 6 different values of the statistic \(\hat{p}_{f}-\hat{p}_{n f}\) are
possible. Table 4.7 shows the number of times each difference occurred among
the 1000 randomizations. Calculate the p-value.
