Female primates visibly display their fertile window, often with red or pink coloration. Do humans also do this? A study 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.