Using Yamane's formula, what is the appropriate sample size for a population of 25,000 with a precision level of 5%?\n63\n345\n394\n4
The Correct Answer and Explanation is:
To determine the appropriate sample size using Yamane’s formula, we apply the following equation:n=N1+N(e)2n = \frac{N}{1 + N(e)^2}n=1+N(e)2N
Where:
- nnn = sample size
- NNN = population size
- eee = level of precision (expressed as a decimal)
Given:
- N=25,000N = 25,000N=25,000
- e=0.05e = 0.05e=0.05 (which corresponds to 5% precision)
Step-by-step calculation:
n=25,0001+25,000(0.05)2n = \frac{25,000}{1 + 25,000(0.05)^2}n=1+25,000(0.05)225,000n=25,0001+25,000(0.0025)n = \frac{25,000}{1 + 25,000(0.0025)}n=1+25,000(0.0025)25,000n=25,0001+62.5n = \frac{25,000}{1 + 62.5}n=1+62.525,000n=25,00063.5n = \frac{25,000}{63.5}n=63.525,000n≈393.7n \approx 393.7n≈393.7
Rounding to the nearest whole number, the sample size is approximately 394.
Correct Answer:
394
Explanation:
Yamane’s formula provides a simplified method to calculate a sample size that ensures sufficient precision for survey-based studies. The 5% precision level means that the margin of error is acceptable at ±5 percentage points. This level is commonly used in research where a moderate level of confidence is sufficient and full enumeration is not feasible.
In this case, applying the formula to a population of 25,000 results in a sample of about 394 respondents. This sample size strikes a balance between manageability and statistical reliability. It ensures that findings from the sample can be generalized to the entire population with a reasonable degree of accuracy. Among the provided options — 63, 345, 394, and 4 — the correct and most appropriate answer is 394.
