Consider the Accompanying 2 $\times$ 3 Table Displaying the Sample Proportions That Fell in the Proportions

question 20

Essay

Consider the accompanying 2 $\times$ 3 table displaying the sample proportions that fell in the various combinations of categories (e.g., 13% of those in the sample were in the first category of both factors). $$\begin{array} { l c c c } \hline & \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } \\\hline \mathbf { 1 } & .13 & .19 & .28 \\\hline \mathbf { 2 } & .07 & .11 & .22 \\\hline\end{array}$$
a. Suppose the sample consisted of n = 100 people. Use the chi-squared test for independence with significance level .10.
b. Repeat part (a) assuming that the sample size was n = 1000.
c. What is the smallest sample size n for which these observed proportions would result in rejection of the independence hypothesis?

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Definitions:

Gate-Control Theory

a theory proposing that the perception of pain is not a direct result of activation of pain receptor neurons, but rather its gate can be closed by signals from the brain.

Large-Fiber Activity

The involvement or action of myelinated nerve fibers that are responsible for transmitting fast and sharp pain signals.

Oval Window

A membrane-covered opening that separates the middle ear from the inner ear and transmits sound vibrations from the ossicles to the cochlea.

Vestibular Sacs

Structures in the inner ear that are responsible for sensing gravity and linear acceleration, helping to maintain balance and spatial orientation.