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

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?