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.

Question

Mathematics

Jace Curtis

7 December, 15:26

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.

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Answers (1)

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Alvin · 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.

Step-by-step 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