In a random sample of 400 registered voters, 120 indicated they plan to vote for Trump for President. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Trump.
A)(0.25, 0.34)
B)(0.27, 0.32)
C)(0.29, 0.30)
D)Cannot be determined from the information given.

Question

Quizplus · Accepted Answer

The proportion of the sample that plans to vote for Trump is 120/400 = 0.30. To calculate the 95% confidence interval for the proportion, we use the formula for the confidence interval of a proportion: $p \pm z\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), and $n$ is the sample size. Plugging in the values, we get $0.30 \pm 1.96\sqrt{\frac{0.30(1-0.30)}{400}}$, which calculates to approximately (0.25, 0.34).

In a Random Sample of 400 Registered Voters, 120 Indicated