Question

The accompanying table is from a study conducted

with the stated objective of addressing cell phone safety by understanding why we use a particular ear for cell phone use. (See “Hemispheric Dominance and Cell Phone Use,” by Seidman, Siegel, Shah, and Bowyer, JAMA Otolaryngology—Head & Neck Surgery,Vol. 139, No. 5.)

The goal was to determine whether the ear choice is associated with auditory or language brain hemispheric dominance. Assume that we want to test the claim that handedness and cell phone ear preference are independent of each other.

a. Use the data in the table to find the expected value for the cell that has an observed frequency of 3. Round the result to three decimal places.

b. What does the expected value indicate about the requirements for the hypothesis test?

	Right Ear	Left Ear	No Preference
Right-Handed	436	166	40
Left-Handed	16	50	3

Short answer

1. Theexpected value for the cell that has an observed frequency of 3 is 4.173.

2. The expected value indicates that the requirements of the hypothesis test are not satisfied.

Step-by-step solution

Given information

The data for ear preference for cell phone use is provided.

Compute the expected value for the cell

a.

Theexpected frequency is computed as,

\(E = \frac{{\left( {row\;total} \right)\left( {column\;total} \right)}}{{\left( {grand\;total} \right)}}\)

The table with row and column total is represented as,

	Right Ear	Left Ear	No Preference	Row total
Right-Handed	436	166	40	642
Left-Handed	16	50	3	69
Column total	452	216	43	711

The expected value for the cell that has an observed frequency of 3 is computed as,

\(\begin{aligned}{c}E = \frac{{\left( {{\rm{69}}} \right)\left( {43} \right)}}{{\left( {711} \right)}}\\ = 4.173\end{aligned}\)

Thus, the expected value for the cell that has an observed frequency of 3 is 4.173.

State what the expected value indicate about the requirements for the hypothesis test

b.

One of the requirements to conduct a hypothesis test using the expected values is that all the expected values must be greater than 5.

From part a) it is observed that the expected value of a cell with value 3 is less than 5.

This implies that the requirements for the hypothesis test are not satisfied.