Asample proportion of 0.44 is found. to determine the margin of error for this statistic, a simulation of 100 trials is run, each with a sample size of 100 and a point estimate of 0.44 the minimum sample proportion from the simulation is 0.32, and the maximum sample proportion from the simulation is 0.50. what is the margin of error of the population proportion using an estimate of the standard deviation?

The margin of error of the population proportion is

Explanation:

The margin of error is given by the formula:


where:
p = sample proportion = 0.44
n = sample size = 100

We need to calculate the z-score, which can be found by the formula:


where:
x = value observed = 0.32 and 0.50
μ = mean value = 0.44
σ = standard deviation

Since the question does not give any information about the standard deviation, we can use the range rule to have an estimate:


Therefore,
σ = (0.50 - 0.32) / 4
   = 0.045

We can now calcuate the z-score:
z₁ = (0.50 - 0.44) / 0.045
    = 1.33
z₂ = (0.32 - 0.44) / 0.045
    = -2.66

The highest the z-score, the highest the level of confidence we will obtain, the wider the interval will be. 

Therefore, we choose z₂ = 2.66 and the margin of error will be:
ME = 2.66·√[0.44·(1 - 0.44) / 100]
      = 0.13

Hence, the margin of error will be +/- 0.13