Use the given data to find the minimum sample size required to estimate a population proportion or percentage.
Margin of error: five percentage points; confidence level 90% from a prior study, ^p is estimated by the decimal equivalent 56%
n= (Round up to the nearest integer)
To find the minimum sample size required to estimate a population proportion or percentage, we can use the formula:
n = (Z^2 * p * (1 - p)) / E^2,
where:
n = minimum sample size,
Z = Z-score corresponding to the desired confidence level,
p = estimated proportion or percentage,
E = margin of error.
In this case, the margin of error is given as five percentage points, which means E = 0.05. The confidence level is 90%, which corresponds to a Z-score of approximately 1.645. The estimated proportion, ^p, is given as 56% or 0.56.
Now we can plug in these values into the formula:
n = ((1.645)^2 * 0.56 * (1 - 0.56)) / (0.05)^2
Simplifying the calculation:
n = (2.706025 * 0.56 * 0.44) / 0.0025
n = 0.64062224 / 0.0025
n ≈ 256.25
Since we cannot have a fraction of a sample, we need to round up to the nearest integer:
n = 257.
Therefore, the minimum sample size required to estimate the population proportion or percentage with a margin of error of five percentage points and a 90% confidence level is 257.
Formula to find sample size:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is found using a z-table for 90% confidence, p = .56, q = 1 - p, ^2 means squared, * means to multiply, and E = .05.
Plug values into the formula and calculate n.