Question

A survey is given in two cities in the same county, Yorktown and Smallville, to estimate the percentage of voters in support of a new stadium. In Yorktown, a simple random sample of 1,200 eligible voters is taken, and it turns out that 975 people support a new stadium. In Smallville, a simple random sample of 1,600 eligible voters is taken, and 1,050 people support a new stadium. Which of the following is the most accurate estimate you can make about the difference in the population proportions p 1 - p 2 ?

A. In the long run, the proportion of voters in favor of a new stadium is about 0.72.
B. People in Yorktown are 15% more likely to vote in favor of a new stadium.
C. It is possible that the true difference in the proportion of Yorktown voters in favor of a new stadium and the proportion of Smallville voters in favor of a new stadium is 0.16.
D. The proportion of all voters in the county who support a new stadium ranges from 0.66 to 0.81.

Answer 1

C. It is possible that the true difference in the proportion of Yorktown voters in favor of a new stadium and the proportion of Smallville voters in favor of a new stadium is 0.16.

Explanation:

• Yorktown

Percentage voters supporting new stadium = 975 / 1200 = 81.25%

• Smallville

Percentage voters supporting new stadium = 1050 / 1600 = 65.625%

• Difference in population proportions supporting new stadium

p1 - p2 = 81.25% - 65.625%

= 15.625% ≈ 16%, i.e 0.16