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Answer :
The margin of error for the population mean weight gain in livestock, with a 99 percent confidence, is approximately ±1.19 pounds.
To calculate the margin of error for the population mean, we can use the formula:
Margin of Error = Critical Value * Standard Deviation / Square Root of Sample Size.
In this case, since the population standard deviation is known (4 pounds) and the sample size is 77 cows, we need to determine the critical value for a 99 percent confidence level.
For a 99 percent confidence level, the critical value (z-score) can be found using a standard normal distribution table. The corresponding z-score is approximately 2.58.
Plugging the values into the formula, we have:
Margin of Error = 2.58 * 4 / √77 ≈ 1.19 pounds.
Therefore, the margin of error for the population mean weight gain in livestock, with a 99 percent confidence, is approximately ±1.19 pounds.
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