Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence,what is the interval estimate for the population proportion (to the nearest 10th of a percent)?
A)78.2% to 81.8%
B)69.2% to 86.4%
C)76.5% to 83.5%
D)77.7% to 82.3%

Question

Quizplus · Accepted Answer

The sample proportion (p) is 1,600/2,000 = 0.8 or 80%. The formula for the confidence interval is $p \pm Z \sqrt{\frac{p(1-p)}{n}}$, where Z is the Z-score for the confidence level (for 95% confidence, Z ≈ 1.96), p is the sample proportion, and n is the sample size. Plugging in the numbers: $0.8 \pm 1.96 \sqrt{\frac{0.8(0.2)}{2000}}$, we get the interval 0.782 to 0.818, or 78.2% to 81.8%.

Suppose 1,600 of 2,000 Registered Voters Sampled Said They Planned