A recent study of 750 zombies in Europe found that 35% of zombies were women. What is the 95% confidence interval of the true proportion of women in Europe who are zombies?
To calculate the 95% confidence interval of the true proportion of women in Europe who are zombies, we can use the formula for the confidence interval for a proportion:
CI = p̂ ± Z * sqrt((p̂(1 - p̂))/n)
Where:
CI = Confidence Interval
p̂ = Sample proportion (35% or 0.35)
Z = Z-score for the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)
n = Sample size (750)
Now let's substitute these values into the formula:
CI = 0.35 ± 1.96 * sqrt((0.35 * (1 - 0.35))/750)
Calculating the expression inside the square root:
sqrt((0.35 * (1 - 0.35))/750) = sqrt(0.35 * 0.65/750) = sqrt(0.22875/750) = sqrt(0.000305)
Now let's substitute it back into the formula:
CI = 0.35 ± 1.96 * sqrt(0.000305)
Calculating the square root:
sqrt(0.000305) = 0.01747
Finally, substitute it back into the formula to calculate the confidence interval:
CI = 0.35 ± 1.96 * 0.01747
Calculating the values:
CI = 0.35 ± 0.03414
Therefore, the 95% confidence interval of the true proportion of women in Europe who are zombies is (0.31586, 0.38414).