Construct A $90 \%$ Confidence Interval For $\left( p _ { 1 } - p _ { 2 } \right)$

question 95

Essay

Construct a $90 \%$ confidence interval for $\left( p _ { 1 } - p _ { 2 } \right)$ when $n _ { 1 } = 400 , n _ { 2 } = 550 , \hat { p } _ { 1 } = .42$ , and $\hat { p } _ { 2 }$ $= .63$ .

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Definitions:

Thermal Inversion Layer

A weather phenomenon where a layer of warm air traps pollution and cooler air beneath it, often leading to poor air quality.

Pollutants

Substances introduced into the environment that cause harm or discomfort to the ecosystem or living organisms.

Nitrogen Dioxide

A toxic, reddish-brown gas that is part of the nitrogen oxides group, contributing to air pollution and respiratory issues.

Organic Compounds

Chemical compounds containing carbon atoms bonded to hydrogen atoms, along with other elements, widely found in living organisms.