To find the sample size value (N) given a desired margin of error (e), we can use the formula:
N = (Z^2 * p * (1-p)) / e^2
Where:
- N is the sample size
- Z is the Z-score corresponding to the desired level of confidence (e.g., for a 95% confidence level, Z ≈ 1.96)
- p is the estimated proportion of the population
- e is the desired margin of error
In this case, the desired margin of error (e) is 0.01 and no information is provided about the estimated proportion of the population (p). Therefore, we can assume a conservative estimate of p = 0.5, which maximizes the sample size and ensures the largest possible sample.
Using the formula, we can calculate the sample size (N):
N = (Z^2 * p * (1-p)) / e^2
N = (1.96^2 * 0.5 * (1-0.5)) / 0.01^2
N = (3.8416 * 0.25) / 0.0001
N = 0.9604 / 0.0001
N ≈ 9604
Therefore, the sample size value (N) is approximately 9604 when the desired margin of error (e) is 0.01.
Answers & Comments
Answer:
9604
Step-by-step explanation:
To find the sample size value (N) given a desired margin of error (e), we can use the formula:
N = (Z^2 * p * (1-p)) / e^2
Where:
- N is the sample size
- Z is the Z-score corresponding to the desired level of confidence (e.g., for a 95% confidence level, Z ≈ 1.96)
- p is the estimated proportion of the population
- e is the desired margin of error
In this case, the desired margin of error (e) is 0.01 and no information is provided about the estimated proportion of the population (p). Therefore, we can assume a conservative estimate of p = 0.5, which maximizes the sample size and ensures the largest possible sample.
Using the formula, we can calculate the sample size (N):
N = (Z^2 * p * (1-p)) / e^2
N = (1.96^2 * 0.5 * (1-0.5)) / 0.01^2
N = (3.8416 * 0.25) / 0.0001
N = 0.9604 / 0.0001
N ≈ 9604
Therefore, the sample size value (N) is approximately 9604 when the desired margin of error (e) is 0.01.