Candidates for political office realize that differ- ent levels of support among men and women may be a crucial factor in determining the outcome of an election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. Find a 95% confidence interval for the difference in the proportions of males and females who will vote for this candidate. Interpret your interval.

Step-by-step explanation:

FOR THE MEN

Given that

n for the men = 473

p for the men = = 0.52

Recall that,

Standard error =

therefore,

SE for men =

                  = 0.023

For 95% CI, z = 1.96

recall that,

CI = p ± z × SE(p)

therefore, CI for men

= 0.52 ± 1.96 ×0.023

= 0.52 ± 0.045

= 0.475 or 0.565

Therefore a 95% CI in that given men population shows that the candidate expects between 47.5% and 56.5% to vote for him.

FOR THE WOMEN

Given that

n for the women = 522

p for the women = = 0.45

referencing the earlier formula,

SE for women =

                 = 0.02177

                 = 0.022

For 95% CI, z = 1.96

recall that,

CI = p ± z × SE(p)

therefore, CI for women

= 0.45 ± 1.96 × 0.022

= 0.45 ± 0.043

= 0.407 or 0.493

Therefore a 95% CI in that given women population shows that the candidate expects between 40.7% and 49.3% to vote for him

it is important to point out that the two intervals overlaps.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.