A Researcher Wishes to Determine Whether the Proportion of American $\mathrm { H } _ { 0 } : \mathrm { p } _1 = \mathrm { p } _ { 2 }$

Essay

A researcher wishes to determine whether the proportion of American women who smoke differs from the proportion of American men who smoke. He wants to test the hypothesis $\mathrm { H } _ { 0 } : \mathrm { p } _1 = \mathrm { p } _ { 2 }$ where p1 represents the proportion of American women who smoke and p2 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 assumptions for a two-proportions z-test satisfied? If not, which assumption is violated and why?