A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They'll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the staff can't know this, but suppose the candidate has a positive image with 60% of males but with only 53% of females. Complete parts a through e below.

a) What sampling design is his staff planning to use?
Multistage
Cluster
Stratified
Systematic

b) What difference would you expect the poll to show?
The proportion of people with a favorable impression of this candidate is expected to be
blank % higher among males or females



c) Of course, sampling error means the poll won't reflect the difference perfectly. What's the standard deviation for the difference in the proportions?

The standard deviation for the difference in the proportions is
blank %.

d) Sketch a sampling model for the size difference in proportions of men and women with favorable impressions of this candidate that might appear in a poll like this. Choose the correct answer below.
A.
A Normal curve is plotted over a horizontal axis labeled from negative 17% to 25% in intervals of 7% and has a peak at 4%. Three areas below the curve between pairs of horizontal coordinates are labeled as follows: from negative 3% to 11%, "68%"; from negative 10% to 18%, "95%"; from negative 17% to 25%, "99.7%."

B.
A Normal curve is plotted over a horizontal axis labeled from negative 1% to 23% in intervals of 4% and has a peak at 11%. Three areas below the curve between pairs of horizontal coordinates are labeled as follows: from 7% to 15%, "68%"; from 3% to 19%, "95%"; from negative 1% to 23%, "99.7%."

C.
A Normal curve is plotted over a horizontal axis labeled from negative 5% to 19% in intervals of 4% and has a peak at 7%. Three areas below the curve between pairs of horizontal coordinates are labeled as follows: from 3% to 11%, "68%"; from negative 1% to 15%, "95%"; from negative 5% to 19%, "99.7%."

e) Could the campaign be misled by the poll, concluding that there really is no gender gap? Explain. Choose the correct answer below.
A.
No; a poll result showing little difference is more than three standard deviations below the expected outcome.
B.
No; a poll result showing little difference is only 1-2 standard deviations below the expected outcome.
C.
Yes; a poll result showing little difference is more than three standard deviations below the expected outcome.
D.
Yes; a poll result showing little difference is only 1-2 standard deviations below the expected outcome.
Click to select your answer(s).