Question

Which of the following correctly calculates the margin of error with a confidence level of 95% for estimating a proportion of blue marbles in a bag, if 21 blue marbles are drawn from a bag with 100 marbles?(1 point)
Responses

0.08
0.08

0.003
0.003

0.01
0.01

0.2
0.2

Answer 1

0.08

Calculation: p̂ = 21/100 = 0.21. SE = sqrt(p̂(1−p̂)/n) = sqrt(0.21·0.79/100) ≈ 0.0407. Margin of error = 1.96·SE ≈ 1.96·0.0407 ≈ 0.08.