To find the minimum sample size required to estimate a population proportion or percentage, we can use the following formula:
n = (ZĀ² * p * q) / EĀ²
Where:
- n is the sample size
- Z is the z-score corresponding to the desired confidence level
- p is the estimated proportion or percentage from previous data (unknown in this case)
- q is the complement of p (1 - p)
- E is the margin of error
In this case, the margin of error is 0.06, and the confidence level is 90%. Since both p and q are unknown, we will assume a worst-case scenario and use p = 0.5 (which maximizes the sample size).
First, we need to find the z-score for a 90% confidence level. The z-score can be found using a standard normal distribution table or a calculator. For a 90% confidence level, the z-score is approximately 1.645.
Now we can calculate the sample size:
n = (1.645Ā² * 0.5 * 0.5) / (0.06Ā²)
n = (2.706025 * 0.25) / 0.0036
n = 0.67650625 / 0.0036
n ā 187.363125
Since we need to round up to the nearest integer, the minimum sample size required to estimate the population proportion or percentage is approximately 188.