Tom Plans to Find A $95 \%$ Confidence Interval Estimate Of $\mathrm { p } 1$

Essay

Tom plans to find a $95 \%$ confidence interval estimate of $\mathrm { p } 1$ , the proportion of women who smoke, and a 95\% confidence interval estimate of $\mathrm { p } _ { 2 }$ , the proportion of men who smoke. He will reject the null hypothesis $\mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ if there is no overlap between the two confidence intervals. Tim plans to find a $95 \%$ confidence interval estimate of $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$ , and will reject the null hypothesis $\mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ if the confidence interval does not include 0 . Will Tom and Tim definitely reach the same conclusion? If not, who is more likely to conclude that there is a significant difference between the two population proportions?