Candidates for political office realize that different 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.
a) Write a 95% confidence interval for the percent of male voters who may vote for this candidate. Interpret your interval.
b) Write a 95% confidence interval for the percent of female voters who may vote for him. Interpret your interval.
c) Do the intervals for males and females overlap? What do you think this means about the gender gap?
d) Find a 95% confidence interval for the difference in the proportions of males and females who will vote for this candidate. Interpret your interval.
e) Does this interval contain zero? What does that mean?
f) Why do the results in parts c and e seem contradictory? If we want to see if there is a gender gap among voters with respect to this candidate, which is the correct approach? Why?