Flemingfarm on Nostr: This is what the AI just spit out. To determine the sample size needed to confirm at ...
This is what the AI just spit out.
To determine the sample size needed to confirm at least 50% of the heifers are pregnant with a 75% confidence level, you can use a formula for calculating sample size for proportions in a finite population.
The formula is:
n = [Z^2 * P(1-P) * N] / [(N-1) * MOE^2 + Z^2 * P(1-P)]
where:
n = sample size
Z = Z-score corresponding to the desired confidence level (for 75% confidence level, Z ≈ 1.15)
P = estimated proportion (0.5 for 50%)
N = population size (25 heifers)
MOE = margin of error
Assuming a margin of error of 0.05 (5%), you can plug in the values:
n = [(1.15)^2 * 0.5 (1-0.5) * 25] / [(25-1) * 0.05^2 + (1.15)^2 * 0.5 (1-0.5)]
n = 2.56 / (24 * 0.0025 + 1.56)
n = 2.56 / (0.06 + 1.56)
n ≈ 2.56 / 1.62
n ≈ 1.58
Therefore, you would need to initially test at least 2 heifers to confirm with 75% confidence that at least 50% of the 25 heifers are pregnant.
Published at
2024-07-07 17:50:02Event JSON
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"content": "This is what the AI just spit out.\n\nTo determine the sample size needed to confirm at least 50% of the heifers are pregnant with a 75% confidence level, you can use a formula for calculating sample size for proportions in a finite population.\n\nThe formula is:\n\nn = [Z^2 * P(1-P) * N] / [(N-1) * MOE^2 + Z^2 * P(1-P)]\n\nwhere:\nn = sample size\nZ = Z-score corresponding to the desired confidence level (for 75% confidence level, Z ≈ 1.15)\nP = estimated proportion (0.5 for 50%)\nN = population size (25 heifers)\nMOE = margin of error\n\nAssuming a margin of error of 0.05 (5%), you can plug in the values:\n\nn = [(1.15)^2 * 0.5 (1-0.5) * 25] / [(25-1) * 0.05^2 + (1.15)^2 * 0.5 (1-0.5)]\nn = 2.56 / (24 * 0.0025 + 1.56)\nn = 2.56 / (0.06 + 1.56)\nn ≈ 2.56 / 1.62\nn ≈ 1.58\n\nTherefore, you would need to initially test at least 2 heifers to confirm with 75% confidence that at least 50% of the 25 heifers are pregnant.",
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