Relative to other nations, how do fourth-graders in the United States rank in terms of reading and math ability? Are they in the bottom 50% or in the top 50%? In a survey of 700 randomly sampled registered voters in the United States conducted by Conquest Communications Group, 258 correctly answered that fourth-graders are in the top 50%. Note: By the age of 15, U.S. students drop to the 50th percentile in reading and below the 25th percentile in mathematics.
(a) Obtain a point estimate for the population proportion of U.S. registered voters who believe fourth-graders rank in the top 50% in reading and math ability.
(b) Verify that the requirements for constructing a confidence interval about p are satisfied.
(c) Construct a 95% confidence interval for the population proportion of U.S. registered voters who answered correctly.
(d) Interpret the interval.