The Sample Size Needed to Estimate the Difference Between Two $\mathrm { E }$

question 82

Multiple Choice

The sample size needed to estimate the difference between two population proportions to within a margin of error $\mathrm { E }$ with a confidence level of $1 - \alpha$ can be found as follows: in the expression
$$\mathrm { E } = \mathrm { z } _ { \alpha } / 2 \sqrt { \frac { \mathrm { p } _ { 1 } \mathrm { q } _ { 1 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { p } _ { 2 } \mathrm { q } _ { 2 } } { \mathrm { n } _ { 2 } } }$$
replace $\mathrm { n } _ { 1 }$ and $\mathrm { n } _ { 2 }$ by $\mathrm { n }$ (assuming both samples have the same size) and replace each of $\mathrm { p } _ { 1 } , \mathrm { q } _ { 1 } , \mathrm { p } _ { 2 }$ , and $\mathrm { q } _ { 2 }$ by $0.5$ (because their values are not known) . Then solve for $\mathrm { n }$ .

Use this approach to find the size of each sample if you want to estimate the difference between the proportions of men and women who plan to vote in the next presidential election. Assume that you want $99 \%$ confidence that your error is no more than $0.05$ .

• A) 1087
• B) 769
• C) 516
• D) 1327

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Definitions:

Low Frequency

Pertains to waves, such as sound or electromagnetic waves, that have a relatively low rate of oscillation or cycles per second.

Place Theory

A theory in psychology that proposes the perception of sound depends on where each component frequency produces vibrations along the basilar membrane of the inner ear.

High-Pitched Sounds

Sounds that have a high frequency, typically perceived as "shrill" by the human ear.

Hair Cells

Sensory cells located in the inner ear, vital for the conversion of sound waves into electrical signals for hearing and helping in the maintenance of balance.