1. Given the population size with their corresponding margin of error, determine the sample size of each of the following (4 points)
a. N = 15,500
e = 5%
b. N = 7,500
e = 6%
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1. Given the population size with their corresponding margin of error, determine the sample size of each of the following (4 points)
a. N = 15,500
e = 5%
b. N = 7,500
e = 6%
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Answer:
To determine the sample size for each scenario we can use the formula:
Sample Size = (Z^2 * p * (1-p)) / (e^2)
Where:
- Z is the Z-score corresponding to the desired confidence level (usually 1.96 for a 95% confidence level).
- p is the estimated proportion of the population.
- e is the desired margin of error.
Let's calculate the sample size for each scenario:
a. N = 15500 e = 5%
For simplicity let's assume the estimated proportion p is 0.5 (which gives the maximum sample size). The Z-score for a 95% confidence level is approximately 1.96.
Sample Size = (1.96^2 * 0.5 * (1-0.5)) / (0.05^2)
Sample Size = 384.16
Therefore the sample size for scenario a is approximately 384.
b. N = 7500 e = 6%
Using the same assumptions p = 0.5 and Z = 1.96.
Sample Size = (1.96^2 * 0.5 * (1-0.5)) / (0.06^2)
Sample Size = 267.11
Therefore the sample size for scenario b is approximately 267.
Note: In practice it is recommended to calculate the sample size based on the estimated proportion for your specific study or using statistical software that can account for the actual population proportion. The assumptions made here are for illustrative purposes only.