Solve the Problem $\mathrm { E }$ With a Confidence Level Of

question 51

Multiple Choice

Solve the problem.
-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
$$E = z _ { \alpha / 2} \sqrt { \frac { p _ { 1 } q _ { 1 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { p } _ { 2 } \mathrm { q } _ { 2 } } { \mathrm { n } _ { 2 } } }$$
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 $n$ .

Use this approach to find the size of each sample if you want to estimate the difference between the proportions . and women who plan to vote in the next presidential election. Assume that you want $99 \%$ confidence that your no more than $0.03$ .

• A) 3017
• B) 2135
• C) 3685
• D) 1432

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Definitions:

Imagined Community

A concept describing how members of a social group or nation perceive themselves as part of a larger community through shared symbols, languages, and media, despite not knowing all members personally.

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Structured groups established for a particular purpose or set of objectives, often characterized by a hierarchy and formal rules.

Bureaucratic Inefficiency

occurs when administrative processes and procedures in organizations or governments are slow, overly complicated, or inefficient, leading to delays and increased costs.

Corporate Hierarchy

The structured organization of management and staff in a company, outlining the levels of responsibility, authority, and command from top executives to lower-level employees.