Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and the 95% confidence interval for the mean weight gain this supplement produces has a margin of error of 11 pounds. Which one of the following interpretations is correct?

A. We are 95% confident that the mean weight gain among all the cows fed by the special feed supplement will be between 45 and 67 pounds.
B. We are 95% confident that a cow fed this supplement will gain between 45 and 67 pounds.
C. We are 95% confident that the mean weight gain among the 77 cows fed by the special feed supplement will be between 45 and 67 pounds.
D. If the supplement is tested on another sample of cows, there is a 95% chance that their average weight gain will be between 45 and 67 pounds.

The correct interpretation of the given information is option C: We are 95% confident that the mean weight gain among the 77 cows fed by the special feed supplement will be between 45 and 67 pounds.

Explanation:

The given information states that the 77 cows studied gained an average of 56 pounds, and the 95% confidence interval for the mean weight gain this supplement produces has a margin of error of 11 pounds.

The correct interpretation of this information is option C: We are 95% confident that the mean weight gain among the 77 cows fed by the special feed supplement will be between 45 and 67 pounds.

This interpretation is based on the fact that a confidence interval is a range of values that is likely to contain the true value of a population parameter. In this case, the confidence interval is calculated based on the sample mean and the margin of error. The 95% confidence level means that if we were to repeat this study multiple times, 95% of the confidence intervals calculated would contain the true mean weight gain of all cows fed the special feed supplement.

Therefore, we can say with 95% confidence that the mean weight gain among the 77 cows studied is between 45 and 67 pounds.

Learn more about interpreting confidence intervals here:

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