When Stalking Gazelles, Cheetah Frequently Have a Choice Between Two

When stalking gazelles, cheetah frequently have a choice between two gazelles close to each other while grazing. A biologist thought the choice of prey might be affected by the "vigilance" behavior of the gazelles. She defined vigilance as the percentage of the time that a gazelle had its head in the air searching for potential predators. She filmed cheetah stalks and analyzed 16 incidents where two same-sex gazelles were within 5 meters of each other; thus, either could have been chosen as the cheetah's prey. The table below presents the vigilance levels for each of the gazelles and the difference (gazelle chased - gazelle ignored) for each pair.
$\begin{array}{|l|c|c|r|l|}\hline&\text { Vigilance of } & \text { Vigilance of } & \text { Difference }\\\text { Pair } & \text { the } & \text { the } & \text { In }& \text {sex }\\\text { \# } & \text { Gazelle } & \text { Gazelle } & \text { Vigilance }\\&\text { Chased } & \text { Ignored } \\\hline\mathbf{1} & 8.0 & 10.0 & -2.0 & \text { Male } \\\mathbf{2} & 31.4 & 78.7 & -47.3 & \text { Male } \\\mathbf{3} & 40.0 & 52.0 & -12.0 & \text { Male } \\\mathbf{4} & 15.7 & 23.9 & -8.2 & \text { Male } \\\mathbf{5} & 40.0 & 81.0 & -41.0 & \text { Male } \\\mathbf{6} & 35.3 & 49.7 & -14.4 & \text { Male } \\\mathbf{7} & 31.7 & 62.0 & -30.3 & \text { Male }\\\mathbf{8} & 68.5 & 72.6 & -4.1 & \text { Male } \\\mathbf{9} & 45.0 & 96.3 & -51.3 & \text { Male } \\\mathbf{1 0} & 39.1 & 90.1 & -51.0 & \text { Male } \\\mathbf{1 1} & 65.2 & 88.3 & -23.1 & \text { Male } \\\mathbf{1 2} & 72.5 & 89.9 & -17.4 & \text { Male } \\\mathbf{1 3} & 17.5 & 65.0 & -47.5 & \text { Female } \\\mathbf{1 4} & 63.0 & 84.2 & -21.2 & \text { Female } \\\mathbf{1 5} & 70.2 & 50.0 & 20.2 & \text { Female } \\\mathbf{1 6} & 38.8 & 20.5 & 18.3 & \text { Female }\\\hline\end{array}$

a) Using the scales below, construct comparative dotplots to show that it is reasonable to use the $t$ -procedure to construct confidence intervals for the difference in population means for males and females.


b) Calculate and interpret the 95% confidence interval in the context of the problem.
c) The investigator noticed that many more male pairs than female pairs were
actually stalked by cheetah. Two theories have been proposed for this difference.
The first theory is that the gazelle females are generally more vigilant than males.
The second theory is that females generally graze near the centers of the herds,
protecting the young, and are less accessible to predators.
i) Is it possible to use investigator's data be used to support or refute the theory
that females are more vigilant than males? Is so, how? If not, why not?
ii) Is it possible to use investigator's data be used to support or refute the theory
that females generally graze near the centers of the herds? Is so, how? If not,
why not?