A Study Investigated the Smoking Status of People in Two $\mathrm { P } 1$

A study investigated the smoking status of people in two age groups.Let $\mathrm { P } 1$ represent the proportion of people aged 20-24 who are smokers.Let $\mathrm { P } 2$ represent the proportion of people aged 25-29 who are smokers.A 95% confidence interval for the difference in smoking rates for $\mathrm { P } 1$ - $\mathrm { P } 2$ was found to be (0.045,0.112) .Give an interpretation of this confidence interval.

A) We know that 95% of the proportion of smokers aged 25-29 is between 4.5% and 11.2% lower than the proportion of smokers aged 20-24.
B) We know that 95% of all random samples done on the population will show that the proportion of smokers aged 20-24 is between 4.5% and 11.2% higher than the proportion of smokers aged 25-29.
C) We are 95% confident that the proportion of smokers aged 25-29 is between 4.5% and 11.2% higher than the proportion of smokers aged 20-24.
D) We know that 95% of the proportion of smokers aged 20-24 is between 4.5% and 11.2% more than the proportion of smokers aged 25-29.
E) We are 95% confident that the proportion of smokers aged 20-24 is between 4.5% and 11.2% higher than the proportion of smokers aged 25-29.