High School

A feed supply company has developed a special feed supplement to see if it will promote weight gain in livestock. Their researchers report that the 77 cows studied gained an average of 56 pounds.

Calculate the margin of error for the population mean with a 99 percent confidence level. Assume the population standard deviation is 4 pounds. (Round to 4 decimal places.)

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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