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

Answer 1

The margin of error can be calculated using the formula:

Margin of error = Z * sqrt[(p*(1-p))/n]

Where:
Z = Z-value for 95% confidence level, which is approximately 1.96
p = proportion of blue marbles in the sample (21/100 = 0.21)
n = total number of marbles in the sample (100)

Plugging in the values:
Margin of error = 1.96 * sqrt[(0.21*(1-0.21))/100]
Margin of error = 1.96 * sqrt[(0.21*0.79)/100]
Margin of error = 1.96 * sqrt[0.1659/100]
Margin of error = 1.96 * sqrt[0.001659]
Margin of error = 1.96 * 0.04074
Margin of error ≈ 0.08

Therefore, the margin of error for estimating the proportion of blue marbles in the bag is approximately 0.08.