Some Animal Behaviorists Study the Evolution of Behavior as a Consequence

Some animal behaviorists study the evolution of behavior as a consequence of natural
selection and the development of species. A common research question involves the
extent to which our human behavior is grounded in an evolutionary past, as opposed
to culturally imposed. For example, among monkey species in Africa, males function
primarily as sentries, warning females that predators are in the area. Might it be so
that human males and females exhibit this behavior? That is, do human males
assume a protective role and human females a protected role? Researchers studied
the look-both-ways behavior of a random sample of females alone and an
independent random sample of females with males at a dangerous pedestrian
crossing. They reasoned that if females assume a protected role, they should look
both ways at a lower proportion when they are with males than when alone. The
resulting data are shown in the table below. $$\begin{array} { | l | c | c | } \hline \text { Social grouping } & \begin{array} { c } \text { Number of } \\\text { crossings }\end{array} & \begin{array} { c } \text { Number looking } \\\text { both ways }\end{array} \\\hline \text { Adult female, alone } & 80 & 60 \\\hline \text { Adult female with adult male } & 76 & 37 \\\hline\end{array}$$ a) What null and alternative hypotheses should the researchers test?
b) It is reasonable to use the large-sample test for a difference in population
proportions. Show that this is true by indicating the necessary calculations.
c) Test the hypothesis you indicated in part (a), and interpret the result in the context
of the study.