A poll was conducted using a sample of 2500 registered voters to determine what proportion of voters are planning to vote for th
e incumbent president in the upcoming election. The pollsters reported, “We are 95% confident that the true proportion of registered voters that will vote for the incumbent president is within the interval 0.465 to 0.545.” What is meant by 95% confidence? (A) The pollsters used a method that is guaranteed to capture the true voting preference of 95% of the registered voters.
(B) The pollsters used a method that will capture the true population proportion in about 95% of all possible confidence intervals based upon random samples of size 2500 from this population.
(C) The pollsters can be 95% confident that the incumbent president will receive 50.5% of the vote and will win the election.
(D) There is a 95% chance that the interval (0.465, 0.545) contains the true proportion of voters that are planning to vote for the incumbent president.
(E) If the pollsters take many random samples of size 2500 from this population, about 95% of the resulting intervals will contain 0.505.
When interpreting a confidence level, we say that if we were to select many random samples of the same size from the same population and construct a 95% confidence interval using each sample, about 95% of the intervals would capture the true proportion of registered voters that plan vote for the incumbent president.
The distance between the points and the y-axis will be the value of the <em>x</em> coordinate, as <em>x</em> is the horizontal distance from 0 and the y-axis.
