The Pre-Historic Development of Agriculture Is an Active Area of Research

The pre-historic development of agriculture is an active area of research among
anthropologists. The transition from a hunter-gatherer society to an agricultural
society is generally assumed to be signaled by an increase in cavities in teeth.
Investigators recently studied teeth unearthed in two societies in Colorado:
Basketmakers, societies living in small villages, and Post-Basketmakers, societies
living in above-ground architectures such as pueblos. The investigators were
interested in whether the shift in shelter was associated with a shift in consumption
from hunting (meat) to agriculture (maize). Data on the numbers of individuals with
interproximal (between teeth) cavities are shown in the table below. Inter-proximal
cavities tend to occur more among populations subsisting primarily on agricultural
products. You may assume that it is reasonable to regard these two samples as
representative of teeth from these two populations. $$\begin{array} { | l | c | c | } \hline \text { Population } & \begin{array} { c } \text { Inter- } \\\text { Proximal } \\\text { Cavities }\end{array} & \begin{array} { c } \text { No Inter- } \\\text { proximal } \\\text { Cavities }\end{array} \\\hline \text { Basketmaker } & 68 & 91 \\\hline \text { Post-Basketmaker } & 60 & 39 \\\hline\end{array}$$ a) Construct and interpret a 90% confidence interval for the difference in population
proportions of individuals with interproximal cavities, Basketmaker - Post-
Basketmaker.
b) Interpret the 90% confidence level
c) Based on your results in parts (a) and (b), would you say that a shift in
consumption patterns is a reasonable conclusion on the part of the investigators?
Justify your response with statistical evidence from parts (a) and/or (b).