Answer :
Final answer:
To estimate the percentage of people who weigh more than 185 pounds in a certain population with a 95% confidence level and a margin of error within 4%, at least 601 people must be sampled.
Explanation:
To estimate the percentage of people who weigh more than 185 pounds in a certain population, we need to determine the sample size required to achieve a 95% confidence level and a margin of error within 4%. We can use the formula for calculating the sample size:
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 (for 95% confidence, Z is approximately 1.96)
- p is the estimated proportion (unknown in this case)
- E is the desired margin of error (4% in this case, which can be expressed as 0.04)
Since we don't know the estimated proportion, we can assume a conservative estimate of 0.5 (50%). Substituting the values into the formula:
n = (1.96^2 * 0.5 * (1-0.5)) / (0.04^2)
Simplifying the equation:
n = (3.8416 * 0.25) / 0.0016
n = 0.9604 / 0.0016
n ≈ 600.25
Rounding up to the nearest whole number, we need to sample at least 601 people to estimate the percentage of people who weigh more than 185 pounds with a 95% confidence level and a margin of error within 4%.
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