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

Understand the types and characteristics of innovations.

Comprehend the process and stages of the diffusion of innovations.

Identify the various categories of adopters in the product adoption process.

Recognize the factors affecting the success and adoption rate of new products.

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Definitions:

Fetus

A developmental stage of a vertebrate that is in the womb or egg, specifically in humans from the ninth week after fertilization until birth.

Blood Pressure

The force exerted by circulating blood on the walls of blood vessels, crucial for maintaining bodily functions.

Mm Hg

Millimeters of mercury; a unit of pressure used in various applications, including the measurement of blood pressure.

Foramen Ovale

A fetal structure allowing blood flow between the right and left atria of the heart, which normally closes after birth.