Solve the Problem $E$ With a Confidence Level of 1 - $\alpha$

question 172

Multiple Choice

Solve the problem.
-The sample size needed to estimate the difference between two population proportions to within a margin of error $E$ with a confidence level of 1 - $\alpha$ can be found as follows: in the expression
$$\mathrm { E } = \mathrm { z } _ { \alpha / 2 } \sqrt { \frac { \mathrm { p } 1 \mathrm { q } _ { 1 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { p } \mathrm { p } _ { 2 } } { \mathrm { n } _ { 2 } } }$$
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 0.02.

• A) 3220
• B) 8289
• C) 6787
• D) 4803

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Definitions:

ATP Synthesis

ATP synthesis refers to the biochemical process through which adenosine triphosphate (ATP), the cell's primary energy carrier, is produced, typically within the mitochondria in aerobic conditions.

Outer Boundary

The external edge or limits of an object, area, or surface.

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The various processes and functions carried out by cells, including energy production, growth, division, and response to external signals.

Anaphase

Time during cell division when chromatids divide (or, in the case of first meiosis, when the chromosome pairs divide).