Question

A box contains 10,000 marbles, of which some are red and the others blue. To estimate the percentage of red marbles in the box, 100 are drawn at random without replacement. Among the draws, 1 turns out to be red. The percentage of red marbles in the box is estimated as 1%, with an SE of 1%. True or false: a 95%-confidence interval for the percentage of red marbles in the box is 1% ± 2%. Explain.

Answer 1

Answer is true

z value at 95% = 1.96

p = 1% , SE = 1%

CI = p +/- z *SE
= 1% + /- 1.96 *1%
= 1% +/- 1.96%
=1% +/- 2% rounding to 1 decimal