A researcher wishes to determine whether the proportion of Canadian women who smoke differs from the proportion of Canadian men who smoke.He wants to test the hypothesis H 0 : p 1 = p 2 \mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 } H 0 : p 1 = p 2 where p 1 \mathrm { p } _ { 1 } p 1 represents the proportion of Canadian women who smoke and P 2 \mathrm { P } _ { 2 } P 2 represents the proportion of Canadian 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-sample z-test for two population proportions met? If not,which assumption is violated and why?

Question

A researcher wishes to determine whether the proportion of Canadian women who smoke differs from the proportion of Canadian men who smoke.He wants to test the hypothesis   H 0 : p 1 = p 2 \mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 } H 0 ​ : p 1 ​ = p 2 ​   where   p 1 \mathrm { p } _ { 1 } p 1 ​   represents the proportion of Canadian women who smoke and   P 2 \mathrm { P } _ { 2 } P 2 ​   represents the proportion of Canadian 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-sample z-test for two population proportions met? If not,which assumption is violated and why?

Nathanael Young · Accepted Answer

Final Answer : The assumptions and conditions necessary for inference are not satisfied.Since married couples were surveyed,the two samples are not independent.

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