Brian Wants to Obtain a Confidence Interval Estimate Of $p _ { 1 } - p _ { 2 }$

question 21

Essay

Brian wants to obtain a confidence interval estimate of $p _ { 1 } - p _ { 2 }$ where $p _ { 1 }$ represents the proportion of American women who smoke and $p _ { 2 }$ represents the proportion of American men who smoke. He randomly selects 100 married couples. Among the 100 women in the sample are 21 smokers. Among the 100 men are 29 smokers. Are the requirements for obtaining a confidence interval estimate of $p _ { 1 } - p _ { 2 }$ satisfied? If not, which requirement is not satisfied?

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Definitions:

Thymus

A gland located behind the sternum and between the lungs that is involved in the development of the body's immune system, particularly in maturing T lymphocytes.

Pre-T Cells

Immature T cells that are in the process of developing into functional T cells, located in the thymus gland.

Functional Immune Cells

Cells of the immune system that are active in defending the body against pathogens and foreign substances.

Macrophages

A type of white blood cell part of the immune system, responsible for detecting, engulfing, and destroying pathogens and dead cells.