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 males alone and an independent
random sample of males with females at a dangerous pedestrian crossing. They
reasoned that if males assume a protective role, they should look both ways at a
higher proportion when they are with females than when alone. The resulting data
are shown in the table below. $$\begin{array} { | l | c | c | }
\hline \text { Social grouping } & \begin{array} { c }
\text { Number of } \
\text { crossings }
\end{array} & \begin{array} { c }
\text { Number looking } \
\text { both ways }
\end{array} \
\hline \text { Adult male, alone } & 84 & 56 \
\hline \text { Adult male with adult female } & 76 & 61 \
\hline
\end{array}$$ a) What are the appropriate null and alternative hypotheses?
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 your result in the
context of the study.

Question

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 males alone and an independent
random sample of males with females at a dangerous pedestrian crossing. They
reasoned that if males assume a protective role, they should look both ways at a
higher proportion when they are with females than when alone. The resulting data
are shown in the table below. $$\begin{array} { | l | c | c | } 
\hline \text { Social grouping } & \begin{array} { c } 
\text { Number of } \
\text { crossings }
\end{array} & \begin{array} { c } 
\text { Number looking } \
\text { both ways }
\end{array} \
\hline \text { Adult male, alone } & 84 & 56 \
\hline \text { Adult male with adult female } & 76 & 61 \
\hline
\end{array}$$ a) What are the appropriate null and alternative hypotheses?
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 your result in the
context of the study.

Quizplus · Accepted Answer

The Answer is a)

p _ { a } =

proportion of males who, when alone, would look both ways

p _ { w } =

proportion of males who, with a female, would look both ways

\begin{array} { l } H _ { 0 } : p _ { a } - p _ { w } = 0 \H _ { a } : p _ { a } - p _ { w } < 0\end{array}

\alpha = .05

b)

\begin{array} { l } n _ { a } p _ { a } = 84 ( 0.6667 ) = 56 \geq 10 \n _ { a } \left( 1 - p _ { a } ight) = 84 ( 1 - 0.6667 ) = 28 \geq 10\end{array}

\begin{array} { l } n _ { w } p _ { w } = 76 ( 0.8026 ) = 61 \geq 10 \n _ { w } \left( 1 - p _ { w } ight) = 76 ( 1 - 0.8026 ) = 15 \geq 10\end{array}

c)
(Picking up after part b...)

p _ { c } = \frac { \left[ n _ { a } p _ { a } + n _ { w } p _ { w } ight] } { n _ { a } + n _ { w } } = \frac { 56 + 61 } { 84 + 76 } = 0.7313

z = \frac { \hat { p } _ { a } - \hat { p } _ { w } } { \sqrt { \frac { \hat { p } _ { c } \left( 1 - \hat { p } _ { c } ight) } { n _ { a } } + \frac { \hat { p } _ { c } \left( 1 - \hat { p } _ { c } ight) } { n _ { w } } } } = \frac { 0.6667 - 0.8026 } { \sqrt { \frac { 0.7313 ( 1 - 0.7313 ) } { 84 } + \frac { 0.7313 ( 1 - 0.7313 ) } { 76 } } }

= - 1.9373

P - ext { Value } = P ( z < - 1.9373 ) = 0.0264

Because the

P

-value is less than .05, I will reject the null hypothesis. There is sufficient evidence to conclude that males look both ways at lower proportion of the time when alone than with males.

Some Animal Behaviorists Study the Evolution of Behavior as a Consequence