Question

simple random sample of voters will be taken in a large state. Researchers will use the methods of our course to construct an approximate 95% confidence interval for the percent of the state’s voters who will vote for Candidate X. The minimum sample size needed to ensure that the width of the interval (right end minus left end) is at most 6% is __________. (Fill in the blank with a positive integer; correct to the nearest 50 is OK.)

Answer 1

focus on sentence minimum sample size required to make the width at-most 6%. hence we can have min. sample size if we have maximum SE which is possible for max interval possible at 0.5.as u have given 95% c.i. its z value is 1.96 and hence i compute it = \[1.96\times \sqrt{( 0.5\times0.5)}\div n = 0.3\]