Question

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.

Answer 1

Answer:

Step-by-step explanation:

FOR THE MEN

Given that

n for the men = 473

p for the men = $\frac{52}{100}$ = 0.52

Recall that,

Standard error = $\sqrt \frac{p(1 - p)}{n}$

therefore,

SE for men = $\sqrt{} \frac{0.52( 1 - 0.52)}{473}$

                  = 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 = $\frac{45}{100}$ = 0.45

referencing the earlier formula,

SE for women = $\sqrt{} \frac{0.45 (1 - 0.45)}{522}$

                 = 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.